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  • Conférence - Paroles aux jeunes chercheurs en dynamique et géométrie
    6 sep 2017 - 8 sep 2017

    Rennes, du 6 septembre au 8 septembre

    Comité d'organisation : Françoise Dal'Bo, Frédéric Paulin, Barbara Schapira, Damien Thomine

    Depuis sa création le réseau Platon (GDR CNRS n°3341 http://costia.free.fr/platon/) mène des actions en direction des jeunes chercheurs dans le domaine de la géométrie ergodique. Les rencontres annuelles " Paroles aux jeunes chercheurs" font partie des temps forts de ce GDR. Elles permettent à une dizaine de doctorants ou de récents docteurs de présenter leurs travaux et de favoriser les échanges entre jeunes chercheurs et chercheurs confirmés. La rencontre « Paroles aux jeunes chercheurs en géométrie et dynamique » s'inscrit dans la lignée de ces rendez-vous récurrents avec une dimension internationale apportée notamment par des réseaux suisses et sénégalais.

    Voir aussi ici

    EXPOSES

    Alexander Adam (UPMC) Resonances for Anosov diffeomorphism

    Kamel Belarif (Université de Bretagne Occidentale) Genericity of weak mixing in negative curvature

    Adrien Boulanger (UPMC) Cascades in affine interval exchanges

    Filippo Cerocchi (Max Planck Institute for Mathematics, Bonn) Rigidity and finiteness for compact 3-manifolds with bounded entropy

    Maria Cumplido Cabello (Université de Rennes 1) Loxodromic actions of Artin-Tits groups

    Nguyen-Bac Dang (Ecole Polytechnique) Degrees of iterates of rational maps

    Laurent Dufloux (Oulu University) Hausdorff dimension of limit sets at the boundary of the complex hyperbolic plane

    Mikolaj Fraczyk (Université Paris-Sud) Mod p homology growth of locally symmetric spaces

    Weikun He (Université Paris-Sud) Sum-product estimates and equidistribution of toral automorphisms

    Cyril Lacoste (Université de Rennes 1) Dimension rigidity of lattices in semisimple Lie groups

    Erika Pieroni (Università di Roma, Sapienza) Minimal Entropy of 3-manifolds

    Fanni M. Selley (Budapest University of Technology) Ergodicity breaking in mean-field coupled map systems

    Nasab Yassine (Université de Bretagne Occidentale) Quantitative recurrence of one-dimensional dynamical systems preserving an infinite measure

    RESUMES

    • Alexander Adam Resonances for Anosov diffeomorphism

    The deterministic chaotic behavior of an invertible map T is appropriately described by the existence of expanding and contracting directions of the differential of T. A special class of such maps consist in Anosov diffeomorphisms. Every 2-by-2 hyperbolic matrix M with integer entries induces such a diffeomorphism on the 2-torus. For all pairs of real-analytic functions on the 2-torus, one defines a correlation function for T which captures the asymptotic independence of such a pair under the evolution T^n as n tends to infinity. What is the rate of convergence of the correlation as n tends to infinity, for instance what is its decay rate? The resonances for T are the poles of the Z-transform of the meromorphic continued correlation function. The decay rate is well-understood if T=M. There are no non-trivial resonances of M. In this talk, I consider small real-analytic perturbations T of M where at least one non-trivial resonance of T appears. This affects the decay rate of the correlation.

    • Kamel Belarif Genericity of weak mixing in negative curvature

    Let M be a manifold with pinched negative sectional curvature. We show that, when M is geometrically finite and the geodesic flow on T^1M is topologically mixing, the set of mixing invariant measures is dense in the set P(T^1M) of invariant probability measures. This implies that the set of weak-mixing measures which are invariant by the geodesic flow is a dense G-delta subset of P(T^1M). We also show how to extend these results to geometrically infinite manifolds with cusps or with constant negative curvature.

    • Adrien Boulanger Cascades in affine interval exchanges

    Avec un échange d'intervalle affine donné vient naturellement une famille de telles dynamiques indexées par le cercle. En effet, la pré-composition par une rotation de l'application initiale définit un autre échange d'intervalle affine. On étudiera cette famille de dynamiques dans un cas particulier à travers la géométrie de la surface affine associée et son groupe de transformation affine.

    An affine interval exchange (AIE) is a piecewise affine map from the circle to itself. Such a map defines a dynamical systems over the circle by iterating it. With an AIE comes naturally a family of AIE indexed by the circle: they are defined by pre-composing the initial AIE by a rotation. The presentation will focus on the study of possible dynamical behaviors of such a family of AIE through a peculiar example.

    • Filippo Cerocchi Rigidity and finiteness for compact 3-manifolds with bounded entropy

    We present some local topological rigidity results for the set S of non-geometric, compact -- with possibly empty boundary and no spherical boundary components --, orientable Riemannian 3-manifolds having torsionfree fundamental group, with bounded entropy and diameter. By "local", we mean that we consider S endowed with the Gromov-Hausdorff-topology. We shall provide examples to show the necessity of the assumptions and discuss some open problems. Moreover, we shall give a proof of the finiteness of the homeomorphism types of the manifolds in S. These are joint works with A. Sambusetti (Rome, Sapienza).

    • Maria Cumplido Cabello Loxodromic actions of Artin-Tits groups

    Artin-Tits groups act on a certain delta-hyperbolic complex, called the ``additional length complex". For an element of the group, acting loxodromically on this complex is a property analogous to the property of being pseudo-Anosov for elements of mapping class groups. A well-known conjecture about mapping class groups claims that "most elements" of the mapping class group of a surface are pseudo-Anosov. In fact, we can prove that a positive proportion is pseudo-Anosov.

    By analogy, we conjecture that ``most'' elements of Artin-Tits groups act loxodromically. More precisely, in the Cayley graph of a subgroup G of an Artin-Tits group, the proportion of loxodromically acting elements in a ball of large radius should tend to one as the radius tends to infinity. We will give a condition guaranteeing that this proportion stays away from zero. This condition is satisfied e.g. for Artin-Tits groups of spherical type, their pure subgroups and some of their commutator subgroups.

    • N'Guyen-Bac Dang Degrees of iterates of rational maps

    In this talk, I will explain what is a rational map, how to define its k-degrees, and I will study the k-degrees of its iterates. I will explain how the study of the growth of these sequences of numbers helps in understanding the dynamics of these maps.

    • Laurent Dufloux Hausdorff dimension of limit sets at the boundary of complex hyperbolic planes

    Consider the standard contact structure on the 3-sphere. The associated subriemannian metric has dimension 4. The Gromov comparison problem asks about how the Hausdorff dimension with respect to this subriemannian metric is related tothe Hausdorff dimension with respect to the usual (Riemannian) metric. We will look at this problem in the case of limit sets of discrete groups of complex hyperbolic isometries.

    • Mikolaj Fraczyk Mod p homology growth of locally symmetric spaces

      I will talk about the growth of the dimension of mod-p homology groups of locally symmetric spaces. Let G be a higher rank Lie group and X its symmetric space and let L be a lattice in G. Results on the rank gradient by Abert, Gelander and Nikolov imply that if L is right angled then for every sequence of subgroups (L_n) of L, the dimensions of the homology groups H_1(X/L_n,Z/pZ) grow sublinearly in the volume of X/L_n. In the special case p=2, I showed that the same statement holds for any sequence of lattices L_n with volume escaping to infinity (even if they are pairwise non-commensurable).

    • Weikun He Sum-product estimates and equidistribution of toral automorphisms

    Bourgain's sum-product theorem is a metric version of Erdős-Szemerédi sum-product theorem. It asserts that a typical set of real numbers grows fast under addition and multiplication. We will present a generalisation of Bourgain's theorem to matrix algebras and discuss how it is motivated by a ergodic problem, namely, quantitative equidistributions of orbits on the d-dimensional torus under sub-semigroups of SL(d,Z).

    • Cyril Lacoste Dimension rigidity of lattices in semisimple Lie groups

    We study actions of discrete groups on classifying spaces (or classifying spaces for proper actions). For instance the hyperbolic plane is a classifying space for proper actions of the group PSL(2,Z) (but not of minimal dimension). Such spaces can be used to compute the cohomology of the group, so we want them to have the lowest possible dimension. This leads us to the definitons of the (proper) geometric dimension and the (virtual) cohomological dimension. These two dimensions are not always equal, we will see it is the case for a lattice in the group of isometries G of a symmetric space of non-compact type without Euclidean factors (such a group is a semisimple Lie group but not necessarily connected). This result has an important consequence called "dimension rigidity", that is, the two dimensions are still equal for a group commensurable to a lattice of G.

    • Erika Pieroni Minimal Entropy of 3-manifolds

    We present the solution of the minimal entropy problem for non-geometric, closed, orientable 3-manifolds (that is, those manifolds which do not admit a com- plete metric locally isometric to one of the eight 3-dimensional model geometries). Together with the results of Besson-Courtois-Gallot for locally symmetric spaces and the work of Soma, Gromov et.al. on the simplicial volume of 3-manifolds and its relation with entropy, this gives a complete picture of the minimal entropy prob- lem for all closed, orientable 3-manifolds. Our work strongly builds on Souto's PhD work (unpublished), filling some gaps in the proof and completing the picture in the case of non-prime manifolds. In detail, we show that the minimal entropy is ad- ditive with respect to the prime decomposition and that for an irreducible manifold X it coincides with the sum of the volume entropies of all the JSJ components of hyperbolic type, each endowed with its complete, hyperbolic metric of nite volume. For the lower bound of MinEnt(X), we adapt Besson-Courtois-Gallot's barycenter method following Souto's ideas; then, we show how this lower bound is realized by producing a sequence of Riemannian metrics gk on X whose volume-entropies tend to

    • Fanni M. SelleyErgodicity breaking in mean-field coupled map systems

    Coupled map systems are simple models of a finite or infinite network of interacting units. The dynamics of the compound system is given by the composition of the (typically chaotic) individual dynamics and a coupling map representing the characteristics of the interaction. The coupling map usually includes a parameter s in [0,1], representing the strength of interaction. The main interest in such models lies in the emergence of bifurcations when s is varied. We first introduce our results for small finite systems. Then we initiate a new point of view which focuses on the evolution of distributions and allows to incorporate the investigation of a continuum of sites.

    • Nasab Yassine Quantitative recurrence of one-dimensional dynamical systems preserving an infinite measure

    We are interested in the asymptotic behaviour of the first return time of the orbits of a dynamical system into a small neighbourhood of their starting points. We study this quantity in the context of dynamical systems preserving an infinite measure. More precisely, we consider the case of Z-extensions of subshifts of finite type. We also consider a toy probabilistic model in order to enlighten the strategy of our proofs.

  • Conférence - Analyse géométrique à Roscoff
    9 oct 2017 - 13 oct 2017

    Roscoff, du 9 octobre au 13 octobre

    Comité d'organisation : Paul Baird, Gilles Carron, Ali Fardoun, Carl Tipler

    Comité scientifique : Gérard Besson (CNRS, Institut Fourier), Olivier Biquard (ENS Paris), Ahmad El Soufi (Univ. Tours)

    L'analyse géométrique est une discipline à l'interface entre l'analyse des équations aux dérivées partielles et de la géométrie riemannienne ; c'est également un outil fondamental en physique mathématique. Cette thématique a connu des développements spectaculaires ces dernières d'années : résolution des conjectures de Poincaré, de Willmore, de Lawson, de Yau-Tian-Donaldson. Ces avancées ont également permis d'élargir la palette des outils utilisés (théorie géométrique de la mesure, définition de la courbure de Ricci pour des espaces métriques, transport optimal...). Cette conférence sera l'occasion de faire rencontrer des spécialistes de différents domaines pour confronter les questions des différents sujets et les outils utilisés.

  • Conférence - Rencontres doctorales Lebesgue 2017
    16 oct 2017 - 18 oct 2017

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    Rennes, du 16 octobre au 18 octobre

    Comité d'organisation : Grégory Boil, Valentin Doli, Caroline Robet, Jérôme Spielmann

    Comité scientifique : Solène Bulteau, Clément Rouffort, Nasab Yassine

    Depuis trois ans, le Centre Henri Lebesgue soutient les Rencontres doctorales Lebesgue, initiative des doctorants du Labex. Il s'agit de trois journées de conférences durant lesquelles la parole est donnée à des doctorants de tout horizon géographique et mathématique. L'objectif est ainsi de présenter un panel le plus large possible de la recherche mathématique actuelle telle qu'elle est vue et vécue par les doctorants, mais pas seulement... Lors de ces rencontres, trois chercheurs, appelés 'parrains' de l'évènement, sont invités à exposer et ainsi à partager leur expérience personnelle de la recherche d'aujourd'hui. Cette année, les rencontres sont parrainées par :

    Jean-Marc Bardet (SAMM, Université Paris 1);

    Jasmin Raissy (Institut mathématique de Toulouse, Université Paul Sabatier);

    Gabriel Rivière (Laboratoire Paul Painlevé, Université Lille 1).

    Bien que principalement destinée aux doctorants, cette conférence se veut également accessible aux étudiants de M2 désireux d’avoir un aperçu des travaux auxquels une thèse en mathématiques peut mener. Pour les doctorants désireux d'exposer leurs travaux de recherche, il est également possible de déposer une proposition sur l'onglet 'Proposer un Exposé'. Dans un souci d'organisation, merci de vous inscrire à l'évènement même si vous proposez un exposé.

  • Complex dynamics and quasi-conformal geometry
    23 oct 2017 - 25 oct 2017

    Our colleague Tan Lei passed away in April 2016. A conference will be held from 23/10/2017 to 25/10/2017 at the University of Angers to honour her memory.

    Scientific Committee

    Etienne Ghys (ENS Lyon)
    John Milnor (Stony Brook)
    Mitsuhiro Shishikura (Kyoto).

    Organizing Committee

    Mohammed El Amrani (Angers)
    Michel Granger(Angers)
    Jean-Jacques Loeb(Angers)
    Laurent Meersseman(Angers)
    Pascale Roesch(Toulouse).

    Provisional list of speakers

    Xavier Buff, Arnaud Cheritat, Nuria Fagella (to be confirmed), Cui Guizhen,Peter Haissinski, John Hamal Hubbard (to be confirmed), Carsten lunde Petersen, Kevin Pilgrim, Mary Rees, Pascale Roesh, Hans Henrik Rugh, Dylan Thurston, Mitsu Shishikura, Giulio Tiozzo.

    More information : page

    The registration process is already open.

  • École - Masterclass 2017
    19 déc 2017 - 21 déc 2017

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    Angers, du 19 décembre au 21 décembre

    Comité d'organisation : Etienne Mann

    We organize a masterclass in Angers, from 19th to 21st of December, 2017.

  • Workshop - Méthodes numériques pour les courbes algébriques
    19 fév 2018 - 23 fév 2018

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    Rennes, du 19 février au 23 février

    Comité d'organisation : Christophe Ritzenthaler

  • Conférence - Journées Maths et entreprise
    12 avr 2018 - 13 avr 2018

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    Vannes, du 12 avril au 13 avril

    Comité d'organisation : Christophe Berthon, Eric Darrigrand, Emmanuel Frénod, Fabrice Mahé

  • École - Éléments finis : théorie et pratique
    16 avr 2018 - 20 avr 2018

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    Roscoff, du 16 avril au 20 avril

    Comité d'organisation : Monique Dauge, Ilaria Peruggia

Conférence - Dynamique en mesure infinie

Brest, du 6 juin au 9 juin

Comité d'organisation : Yves Coudène, François Maucourant, Françoise Pène, Barbara Schapira, Samuel Tapie, Annick Nicolle

Comité scientifique : Jon Aaronson, Jean-Pierre Conze, Gilles Courtois, Domokos Szasz

Cette conférence est centrée sur l’étude des systèmes dynamiques qui préservent une mesure naturelle dont la masse totale est infinie. Ces systèmes peuvent être de nature géométrique, provenir des sciences naturelles ou avoir une origine probabiliste. Lorsque la mesure invariante n’est plus finie, la récurrence n’est plus garantie, le mélange ne subsiste plus sous sa forme habituelle et de nouvelles propriétés asymptotiques (par exemple l’ergodicité rationnelle) se manifestent. Ceci conduit à des comportements pour les systèmes à la fois plus divers et plus subtils qu’en mesure finie.

Cette conférence a pour but de réunir des experts du sujet au plan international ainsi que de permettre un accès aux jeunes chercheurs aux nombreux travaux en cours sur ces thématiques.

Voir aussi ici here

EXPOSES

Jon Aaronson (Tel Aviv Univ.),

Sara Brofferio (Univ. Paris Sud),

Mickael Bromberg (Univ. Bristol)

Jon Chaika (Univ. Utah),

Françoise Dal'bo (Univ. Rennes 1),

Dmitry Dolgopyat (Univ. Maryland),

Rhiannon Dougall (Univ. Warwick),

Olivier Glorieux (Luxembourg),

Sebastien Gouëzel (Univ. Nantes),

Alba Malaga Sabogal (Univ. Paris 8),

Emmanuel Roy (Univ. Paris 13),

Manuel Stadlbauer (Univ. Federal Rio de Janeiro),

Dalia Terhesiu (Univ. Vienna),

Damien Thomine (Univ. Paris Sud),

Roland Zweimüller (Univ. Vienna).

Titres et résumés

Jon Aaronson (Tel Aviv Univ.) Rational ergodicity properties and distributional limits of infinite ergodic transformations.

In infinite ergodic theory, various weak and distributional limits replace the absolutely normalized pointwise ergodic theorem. We’ll review the subject and then see that every random variable on the positive reals occurs as the distributional limit of some infinite ergodic transformation. As a corollary, we obtain a complete classification of the possible ”A-rational ergodicity properties” for an infinite ergodic transformation.

The main construction follows by ”inversion” from a cutting and stacking construction showing that every random variable on the positive reals occurs as the distributional limit of the partial sums some positive, ergodic stationary process normalized by a 1-regularly varying normalizing sequence (indeed, here the process can be chosen over any EPPT).

Joint work with Benjamin Weiss. See arXiv:1604.03218

Sara Brofferio (Univ. Paris Sud), On unbounded invariant measures of stochastic dynamical systems

We consider stochastic dynamical systems Xn = Yn(Xn−1), where Yn are i.i.d. random continuous transformations of R. We assume that Yn(x) behave asymptotically like Anx, for some random positive number An. The main example is the stochastic affine recursion Xn = AnXn−1+Bn, but this class includes other interesting processes such as reflecting random walks or branching process. Our aim is to describe invariant Radon measures of the process {Xn} in the critical case, when ElogA = 0. Under optimal assumptions, we prove that those measures behave at infinity like dx/x. In the proof we strongly use some properties of random walks on the affine group. The talk will be based on a joint paper with Dariusz Buraczewski.

Jon Chaika (Univ. Utah), Ergodicity of typical skew products over some interval exchange transformations

Let T be a linear recurrent interval exchange transformation. This is ameasure zero, but full Hausdorff dimension set of interval exchange transformations that are analogous to badly approximable rotations. We show that an R valued skew product over such an IET by an integral 0 function that is a linear combination of characteristic functions of intervals is typically ergodic. Relevant terms will be defined. This is joint work with Donald Robertson.

Françoise Dal’bo (Univ. Rennes 1), An example of a nonuniform lattice with infinite Bowen-Margulis measure

Joint work with M.Peign´e, J-C Picaud,A.Sambusetti. I will explain how to construct a noncompact negatively curved Riemannian surface with finite volume admitting an infinite Bowen-Margulis measure.

Dmitry Dolgopyat (Univ. Maryland) On Local Limit Theorems for hyperbolic flows

I describe an approach to proving local limit theorems and related for flows based on (multidimensional) local limit theorem for associated Poincare map. Both finite and infinite measure case will be discussed. Based on a joint work with Peter Nandori.

Rhiannon Dougall (Univ. Warwick) Growth of closed geodesics for infinite covers

We are interested in the dynamics of the geodesic flow for infinite volume manifolds M which arise as a regular cover of a fixed compact (or convex cocompact) negatively curved manifold M0. Writing hM for the exponential growth rate of closed geodesics in M, we have that hM ≤ h0, where h0 is the topological entropy of the geodesic flow for M0. We answer the question of when there is a uniform gap hM < h0 in M in terms of the permutation representations given by the covering M of M0. The proof uses the symbolic dynamics for the flow, and so we formulate the analogous statements for countable state shifts obtained as group extensions of a finite state shift.

Olivier Glorieux (IMPA) Hausdorff dimension and critical exponent of Quasi-Fuchsian Anti-de Sitter manifolds

The aim of my talk will be to explain how classical invariants and theorems for groups acting on the hyperbolic space, can be extended to the Anti-de Sitter (AdS) setting. We will recall the notion of critical exponent and Hausdorff dimension for discrete action on the hyperbolic space and explain how we can define similar notions for a certain type of groups acting on AdS manifolds. We will finally explain how to get a rigid bound for these invariants in dimension 3 which is a result equivalent a famous result obtained by R. Bowen in ’79 . This is a joint work with D. Monclair.

Sébastien Gouëzel Quantitative Pesin theory for subshifts of finite type

In non-uniformly hyperbolic dynamics, Pesin sets are measurable sets where the dynamics is very well understood. However, their definition makes these sets hard to control in a quantitative way, even when the underlying dynamics is hyperbolic. We will explain why such a control is useful, and what kind of bounds we can obtain. Joint work with L. Stoyanov.

Alba Málaga Sabogal Generic Wind-Tree Dynamics

The Wind-Tree is an example of a dynamical system that has a very simple description, while having a very rich dynamics. It’s a particular case of a billiard: a particle (the wind) goes straight forward as long as it does not meet any obstacle and it bounces elastically at each obstacle met. There is an infinite number of square obstacles which are distributed irregularly all over the plane. The dynamics will strongly depend on the distribution of the obstacles. The different configurations live in a Baire space - we can thus ask what happens for a generic configuration (i.e. a configuration in a G δ -dense set). We found that generic Wind Tree dynamics is actually nice: minimal, ergodic and of infinite ergodic index in almost every direction. This is joint work with Serge Troubetzkoy.

Emmanuel Roy (Univ. Paris 13) Ergodic splittings of Poisson processes

If N denotes a Poisson process, a splitting of N is formed by two point processes N1 and N2 such that N = N1 +N2. If N1 and N2 are independent Poisson processes then the splitting is said to be Poisson and such a splitting is always available (We allow the possibility to enlarge the ambient probability space). In general, a splitting is not Poisson but the situation changes if we require that the distributions of the point processes are invariant by a common underlying map that acts at the level of each point of the processes. We will prove that if this map has infinite ergodic index, then a splitting is necessarily Poisson if the environment is ergodic.

This is a work in progress, with Elise Janvresse and Thierry de la Rue.

Manuel Stadlbauer Graph extensions of Gibbs-Markov maps and amenability

The aim of the talk is to relate a general notion of amenability of graphs with the probability of return of a random walk with stationary increments. That is, for a Markov map T : X → X with embedded Gibbs-Markov structure (i.e. T is a tower over a Gibbs-Markov map with full branches) and κ a map from X to the automorphisms of the graph, we relate the decay of μ ({x :κ(T n(x))⋅⋅⋅κ (T(x)) ∘κ(x)(o)= o}) with the amenability of the graph. It turns out that on the level of the embedded Gibbs-Markov structure, amenability is equivalent to spectral radius equal to 1 of the transfer operator of the graph extension. In particular, this generalizes results by Kesten, Day and Derriennic and Guivarc’h for random walks with independent increments. With respect to T , the relation is more intricate and requires additional assumptions. These results have canonical application to the geodesic flow on H∕G, where G is a subgroup of a finitely generated Fuchsian group.

This is joint work with Johannes Jaerisch (Shimane, Japan) and Elaine Rocha (Salvador, Brazil).

Dalia Terhesiu, Exploiting semistable laws for i.id. random variables

We recall that semistable laws is a class of infinitely divisible laws, which complements the more well known stable laws. I will recall some main, previously established, results on necessary and sufficient conditions for the existence of semistable laws for i.id. random variables. I will report on work in progress with Peter Kevei which aims toward a complete understanding of a limit law for null recurrent renewal chains, assuming that the involved return function is in the domain of a semistable law (as such, no strict regular variation is required). Some analogies with the Darling Kac law will be discussed. If time remains, I will present some results of work in progress with Douglas Coates on semistable laws for interval intermittent maps.

Damien Thomine Induction invariance, harmonic functions and applications

Given a random walk on Zd, one may be interested in a large variety of questions on its statistical porperties (such as ”What is the probability of being at a given site at a given time?”). Here, I shall discuss questions such as:

  • Starting from 0, what is the probability of hitting site p before going back to 0?

  • Starting from 0, what is the probability of hitting site p before site q?

In the setting of random walks, the answer to these questions is well known, and involves the induction invariance of the solutions of the Poisson equation.

In the setting of Zd extensions of dynamical systems, however we lose the Markov property, and thus we cannot use these tools. However, I’ll show that these can be partially replaced by a use of Green-Kubo’s formula, which still satisfies some induction invariance in this more general setting. This gives us answers for dynamical systems such as the geodesic flow on periodic hyperbolic surfaces, or (in part) Lorentz’ gases.

Joint work with F. Pène (University of Brest).

Roland Zweimüller Return- and hitting-time distributions of small sets.

I will present some work on the asymptotics of return- and hitting-time distributions of small sets in certain infinite measure preserving systems, as the measure of these sets decreases to zero (“rare events”). My focus will be on fairly nice concrete systems and an abstract setup accommodating them. This includes joint work with F. Pene, B. Saussol, and S. Rechberger.

Partenaires

Irmar LMJL ENS Rennes LMBA LAREMA

Tutelles

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENSRennes UBO UBS Angers UBL