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I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, and iceberg model.[-]

I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, ...[+]

37B50 ; 37B10 ; 37B40

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I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, and iceberg model.[-]

I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, ...[+]

37B50 ; 37B10 ; 37B40

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We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

37D50 ; 37C30 ; 37B40

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Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to specification" using a decomposition of the space of finite-length orbit segments, and then survey various applications, including factors of beta-shifts, derived-from-Anosov diffeomorphisms, and geodesic flows in non-positive curvature and beyond.[-]

Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to s...[+]

37D35 ; 37B10 ; 37B40

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Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to specification" using a decomposition of the space of finite-length orbit segments, and then survey various applications, including factors of beta-shifts, derived-from-Anosov diffeomorphisms, and geodesic flows in non-positive curvature and beyond.[-]

Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to s...[+]

37D35 ; 37B10 ; 37B40

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Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to specification" using a decomposition of the space of finite-length orbit segments, and then survey various applications, including factors of beta-shifts, derived-from-Anosov diffeomorphisms, and geodesic flows in non-positive curvature and beyond.[-]

Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to s...[+]

37D35 ; 37B10 ; 37B40

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In this talk, we will discuss various growth rates associated to Anosov flows and their covers. The topological entropy of an Anosov flow on a compact manifold is realised as the exponential growth rate of its periodic orbits. If we pass to a regular cover of the manifold then we can consider a corresponding growth rate for the lifted flow. This growth is bounded above by the topological entropy but if the cover is infinite then the growth rate may be strictly smaller. For abelian covers, this phenomenon admits a precise description in terms of a variational principle. More recent work, joint with Rhiannon Dougall, considers more general infinite covers.[-]

In this talk, we will discuss various growth rates associated to Anosov flows and their covers. The topological entropy of an Anosov flow on a compact manifold is realised as the exponential growth rate of its periodic orbits. If we pass to a regular cover of the manifold then we can consider a corresponding growth rate for the lifted flow. This growth is bounded above by the topological entropy but if the cover is infinite then the growth rate ...[+]

37D20 ; 37D35 ; 37D40 ; 37B40

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There are various classical and more recent decomposition results in mapping class group theory, geometric group theory, and complex dynamics (which include celebrated results by Bill Thurston). We will discuss several natural decompositions that arise in the study of rational maps, such as Pilgrim's canonical decomposition and Levy decomposition (by Bartholdi and Dudko). I will also introduce a new decomposition of rational maps based on the topology of their Julia sets (obtained jointly with Dima Dudko and Dierk Schleicher). At the end of the talk, we will briefly consider connections of this novel decomposition to geometric group theory and self-similar groups.[-]

There are various classical and more recent decomposition results in mapping class group theory, geometric group theory, and complex dynamics (which include celebrated results by Bill Thurston). We will discuss several natural decompositions that arise in the study of rational maps, such as Pilgrim's canonical decomposition and Levy decomposition (by Bartholdi and Dudko). I will also introduce a new decomposition of rational maps based on the ...[+]

37F10 ; 37F20 ; 37B10 ; 37B40 ; 20F67 ; 20E08

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The automorphism group of a compact Kähler manifold satisfies Tits alternative: any subgroup either admits a solvable subgroup of finite index or contains a free non-abelian group of two generators (Campana-WangZhang). In the first case, this group cannot be too big. Some algebraic (rational) manifolds with special automorphisms admit infinitely many nonequivalent real forms. This talk is based on my (old and recent) works with F. Hu, H.-Y. Lin, V.-A. Nguyen, K. Oguiso, N. Sibony, X. Yu, D.-Q. Zhang.[-]

The automorphism group of a compact Kähler manifold satisfies Tits alternative: any subgroup either admits a solvable subgroup of finite index or contains a free non-abelian group of two generators (Campana-WangZhang). In the first case, this group cannot be too big. Some algebraic (rational) manifolds with special automorphisms admit infinitely many nonequivalent real forms. This talk is based on my (old and recent) works with F. Hu, H.-Y. Lin, ...[+]

14J50 ; 32M05 ; 32H50 ; 37B40

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Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for rotation sets of toral homeomorphisms, exponential growth of periodic orbits and estimates on topological entropy of maps.[-]

Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for ...[+]

37E30 ; 37E45 ; 37B40

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Documents 37B40 17 résultats

Entropy and mixing for multidimensional shifts of finite type - Lecture 1 - Pavlov, Ronnie (Auteur de la Conférence) | CIRM H Nouveau

Entropy and mixing for multidimensional shifts of finite type - Lecture 2 - Pavlov, Ronnie (Auteur de la Conférence) | CIRM H Nouveau

Transfer operators for Sinai billiards - lecture 3 - Baladi, Viviane (Auteur de la Conférence) | CIRM H Nouveau

Beyond Bowen specification property - lecture 1 - Climenhaga, Vaughn (Auteur de la Conférence) | CIRM H Nouveau

Beyond Bowen specification property - lecture 2 - Climenhaga, Vaughn (Auteur de la Conférence) | CIRM H Nouveau

Beyond Bowen specification property - lecture 3 - Climenhaga, Vaughn (Auteur de la Conférence) | CIRM H Nouveau

Entropy and growth of periodic orbits for Anosov flows and their covers - Sharp, Richard (Auteur de la Conférence) | CIRM H Nouveau

Decomposition results in rational dynamics - Hlushchanka, Mikhail (Auteur de la Conférence) | CIRM H Nouveau

On the automorphisms of compact Kähler manifolds - Dinh, Tien-Cuong (Auteur de la Conférence) | CIRM H Nouveau

Forcing theory for transverse trajectories of surface homeomorphisms - Part 3 - Tal, Fabio (Auteur de la Conférence) | CIRM H Nouveau