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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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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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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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Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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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Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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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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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I will talk about a joint work with Novikov on 'complex cells', which are a complexification of the cells/cylinders used in o-minimality theory. It turns out that complex cells admit a canonical hyperbolic metric which is not directly accessible in the real setting, leading to a much richer structure theory. In particular, complex cells are closer than real cells to resolution of singularities - and many of their basic properties are inspired by this connection. Our main motivation for introducing complex cells was to prove a sharper form of the Yomdin-Gromov lemma, leading to some applications in dynamics and number theory. I will outline how complex cells can be used to achieve this, and in particular how their hyperbolic structure leads to much sharper constructions compared to the previously existing methods.[-]

I will talk about a joint work with Novikov on 'complex cells', which are a complexification of the cells/cylinders used in o-minimality theory. It turns out that complex cells admit a canonical hyperbolic metric which is not directly accessible in the real setting, leading to a much richer structure theory. In particular, complex cells are closer than real cells to resolution of singularities - and many of their basic properties are inspired by ...[+]

14P10 ; 37B40 ; 03C64 ; 30C99

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I will talk about a joint work with Novikov on 'complex cells', which are a complexification of the cells/cylinders used in o-minimality theory. It turns out that complex cells admit a canonical hyperbolic metric which is not directly accessible in the real setting, leading to a much richer structure theory. In particular, complex cells are closer than real cells to resolution of singularities - and many of their basic properties are inspired by this connection. Our main motivation for introducing complex cells was to prove a sharper form of the Yomdin-Gromov lemma, leading to some applications in dynamics and number theory. I will outline how complex cells can be used to achieve this, and in particular how their hyperbolic structure leads to much sharper constructions compared to the previously existing methods.[-]

I will talk about a joint work with Novikov on 'complex cells', which are a complexification of the cells/cylinders used in o-minimality theory. It turns out that complex cells admit a canonical hyperbolic metric which is not directly accessible in the real setting, leading to a much richer structure theory. In particular, complex cells are closer than real cells to resolution of singularities - and many of their basic properties are inspired by ...[+]

14P10 ; 37B40 ; 03C64 ; 30C99

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

I will talk about a joint work with Novikov on 'complex cells', which are a complexification of the cells/cylinders used in o-minimality theory. It turns out that complex cells admit a canonical hyperbolic metric which is not directly accessible in the real setting, leading to a much richer structure theory. In particular, complex cells are closer than real cells to resolution of singularities - and many of their basic properties are inspired by this connection. Our main motivation for introducing complex cells was to prove a sharper form of the Yomdin-Gromov lemma, leading to some applications in dynamics and number theory. I will outline how complex cells can be used to achieve this, and in particular how their hyperbolic structure leads to much sharper constructions compared to the previously existing methods.[-]

I will talk about a joint work with Novikov on 'complex cells', which are a complexification of the cells/cylinders used in o-minimality theory. It turns out that complex cells admit a canonical hyperbolic metric which is not directly accessible in the real setting, leading to a much richer structure theory. In particular, complex cells are closer than real cells to resolution of singularities - and many of their basic properties are inspired by ...[+]

14P10 ; 37B40 ; 03C64 ; 30C99

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Documents 37B40 17 résultats

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

Transfer operators for Sinai billiards - lecture 1 - Baladi, Viviane (Auteur de la Conférence) | CIRM H Nouveau

Transfer operators for Sinai billiards - lecture 2 - Baladi, Viviane (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

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

Complex cellular structures - Lecture 1 - Binyamini, Gal (Auteur de la Conférence) | CIRM H Nouveau

Complex cellular structures - Lecture 2 - Binyamini, Gal (Auteur de la Conférence) | CIRM H Nouveau

Complex cellular structures - Lecture 3 - Binyamini, Gal (Auteur de la Conférence) | CIRM H Nouveau