Documents  37C40 | enregistrements trouvés : 28

Research schools;Dynamical Systems and Ordinary Differential Equations

These lectures are a mostly self-contained sequel to Vaughn Climenhaga’s talks in week 1. The focus of the week 2 lectures will be on uniqueness of equilibrium states for rank 1 geodesic flows, and their mixing properties. Burns, Climenhaga, Fisher and myself showed recently that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. I will discuss the proof of this result. With this result in hand, the question of when the “pressure gap” hypothesis can be verified becomes crucial. I will sketch our proof of the “entropy gap”, which is a new direct constructive proof of a result by Knieper. I will also describe new joint work with Ben Call, which shows that all the unique equilibrium states provided above have the Kolmogorov property. When the manifold has dimension at least 3, this is a new result even for the Knieper-Bowen-Margulis measure of maximal entropy. The common thread that links all of these arguments is that they rely on weak orbit specification properties in the spirit of Bowen. These lectures are a mostly self-contained sequel to Vaughn Climenhaga’s talks in week 1. The focus of the week 2 lectures will be on uniqueness of equilibrium states for rank 1 geodesic flows, and their mixing properties. Burns, Climenhaga, Fisher and myself showed recently that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. I will discuss the proof of this result. With this result in hand, ...

37D35 ; 37D40 ; 37C40 ; 37D25

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Research schools;Dynamical Systems and Ordinary Differential Equations

These lectures are a mostly self-contained sequel to Vaughn Climenhaga’s talks in week 1. The focus of the week 2 lectures will be on uniqueness of equilibrium states for rank 1 geodesic flows, and their mixing properties. Burns, Climenhaga, Fisher and myself showed recently that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. I will discuss the proof of this result. With this result in hand, the question of when the “pressure gap” hypothesis can be verified becomes crucial. I will sketch our proof of the “entropy gap”, which is a new direct constructive proof of a result by Knieper. I will also describe new joint work with Ben Call, which shows that all the unique equilibrium states provided above have the Kolmogorov property. When the manifold has dimension at least 3, this is a new result even for the Knieper-Bowen-Margulis measure of maximal entropy. The common thread that links all of these arguments is that they rely on weak orbit specification properties in the spirit of Bowen. These lectures are a mostly self-contained sequel to Vaughn Climenhaga’s talks in week 1. The focus of the week 2 lectures will be on uniqueness of equilibrium states for rank 1 geodesic flows, and their mixing properties. Burns, Climenhaga, Fisher and myself showed recently that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. I will discuss the proof of this result. With this result in hand, ...

37D35 ; 37D40 ; 37C40 ; 37D25

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Research schools;Dynamical Systems and Ordinary Differential Equations

These lectures are a mostly self-contained sequel to Vaughn Climenhaga’s talks in week 1. The focus of the week 2 lectures will be on uniqueness of equilibrium states for rank 1 geodesic flows, and their mixing properties. Burns, Climenhaga, Fisher and myself showed recently that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. I will discuss the proof of this result. With this result in hand, the question of when the “pressure gap” hypothesis can be verified becomes crucial. I will sketch our proof of the “entropy gap”, which is a new direct constructive proof of a result by Knieper. I will also describe new joint work with Ben Call, which shows that all the unique equilibrium states provided above have the Kolmogorov property. When the manifold has dimension at least 3, this is a new result even for the Knieper-Bowen-Margulis measure of maximal entropy. The common thread that links all of these arguments is that they rely on weak orbit specification properties in the spirit of Bowen. These lectures are a mostly self-contained sequel to Vaughn Climenhaga’s talks in week 1. The focus of the week 2 lectures will be on uniqueness of equilibrium states for rank 1 geodesic flows, and their mixing properties. Burns, Climenhaga, Fisher and myself showed recently that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. I will discuss the proof of this result. With this result in hand, ...

37D35 ; 37D40 ; 37C40 ; 37D25

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Research talks;Dynamical Systems and Ordinary Differential Equations

We prove a couple of general conditional convergence results on ergodic averages for horocycle and
geodesic subgroups of any continuous $SL(2,\mathbb{R})$- action on a locally compact space. These results are motivated by theorems of Eskin, Mirzakhani and Mohammadi on the $SL(2,\mathbb{R})$-action on the moduli space of Abelian differentials. By our argument we can derive from these theorems an improved version of the “weak convergence” of push-forwards of horocycle measures under the geodesic flow and a new short proof of a theorem of Chaika and Eskin on Birkhoff genericity in almost all directions for the Teichmüller geodesic flow. We prove a couple of general conditional convergence results on ergodic averages for horocycle and
geodesic subgroups of any continuous $SL(2,\mathbb{R})$- action on a locally compact space. These results are motivated by theorems of Eskin, Mirzakhani and Mohammadi on the $SL(2,\mathbb{R})$-action on the moduli space of Abelian differentials. By our argument we can derive from these theorems an improved version of the “weak convergence” of ...

37D40 ; 37C40 ; 37A17

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Research talks;Dynamical Systems and Ordinary Differential Equations

I will survey recent results on the generic properties of probability measures invariant by the geodesic flow defined on a nonpositively curved manifold. Such a flow is one of the early example of a non-uniformly hyperbolic system. I will talk about ergodicity and mixing both in the compact and noncompact setting, and ask some questions about the associated frame flow, which is partially hyperbolic.

37B10 ; 37D40 ; 34C28 ; 37C20 ; 37C40 ; 37D35

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Research schools;Dynamical Systems and Ordinary Differential Equations

Works by Sarig and Benovadia have built symbolic dynamics for arbitrary diffeomorphisms of compact manifolds. This shows thatthere can be at most countably many ergodic hyperbolic equilibriummeasures for any Holder continuous or geometric potentials. We will explain how this yields uniqueness inside each homoclinic class of measures, i.e., of ergodic and hyperbolic measures that are homoclinically related. In some cases, further topological or geometric arguments can show global uniqueness.
This is a joint work with Sylvain Crovisier and Omri Sarig Works by Sarig and Benovadia have built symbolic dynamics for arbitrary diffeomorphisms of compact manifolds. This shows thatthere can be at most countably many ergodic hyperbolic equilibriummeasures for any Holder continuous or geometric potentials. We will explain how this yields uniqueness inside each homoclinic class of measures, i.e., of ergodic and hyperbolic measures that are homoclinically related. In some cases, further topological or ...

37C40

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Research schools;Dynamical Systems and Ordinary Differential Equations

Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We will give two new applications: - for any C∞ surface diffeomorphism f with positive entropy the saddle periodic points with Lyapunov exponents $\delta$-away from zero for $\delta \in]0,htop(f)[$ are equidistributed along measures of maximal entropy. - for C∞ maps the entropy is physically greater than or equal to the top Lyapunov exponents of the exterior powers. Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We will give two new applications: - for any C∞ surface diffeomorphism f with positive entropy the saddle periodic points with Lyapunov exponents $\delta$-away ...

37C05 ; 37C40 ; 37D25

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Research schools;Dynamical Systems and Ordinary Differential Equations

Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We will give two new applications: - for any C∞ surface diffeomorphism f with positive entropy the saddle periodic points with Lyapunov exponents $\delta$-away from zero for $\delta \in]0,htop(f)[$ are equidistributed along measures of maximal entropy. - for C∞ maps the entropy is physically greater than or equal to the top Lyapunov exponents of the exterior powers. Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We will give two new applications: - for any C∞ surface diffeomorphism f with positive entropy the saddle periodic points with Lyapunov exponents $\delta$-away ...

37C05 ; 37C40 ; 37D25

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Research schools;Dynamical Systems and Ordinary Differential Equations

Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We will give two new applications: - for any C∞ surface diffeomorphism f with positive entropy the saddle periodic points with Lyapunov exponents $\delta$-away from zero for $\delta \in]0,htop(f)[$ are equidistributed along measures of maximal entropy. - for C∞ maps the entropy is physically greater than or equal to the top Lyapunov exponents of the exterior powers. Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We will give two new applications: - for any C∞ surface diffeomorphism f with positive entropy the saddle periodic points with Lyapunov exponents $\delta$-away ...

37C05 ; 37C40 ; 37D25

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- xvi; 353 p.
ISBN 978-3-540-87524-6

Springer monographs in mathematics

Localisation : Ouvrage RdC (PINT)

difféomorphisme # difféomophisme hyperbolique # variétés invariantes # lamination # ratios de Hölder # fonction solénoïde # renormalisation # holonomie # mesure de Gibbs

37A05 ; 37A20 ; 37A25 ; 37A35 ; 37C05 ; 37C15 ; 37C27 ; 37C40 ; 37C70 ; 37C75 ; 37C85 ; 37E05 ; 37E10 ; 37E15 ; 37E20 ; 37E25 ; 37E30 ; 37E45 ; 37D99 ; 37A99 ; 37B99 ; 37-02

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- 122 p.
ISBN 978-3-03719-003-6

Zurich lectures in advanced mathematics

Localisation : Ouvrage RdC (PESI)

système dynamique # hyperbolicité partielle # ergodicité stable # système hyperbolique non-uniforme # exposant de Lyapunov # foliation # continuité # système dynamique continu

37-02 ; 37D25 ; 37C40 ; 37A30 ; 37D40

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- 138 p.
ISBN 978-3-540-40121-6

Springer monographs in mathematics

Localisation : Ouvrage RdC (MARG)

système dynamique # courbure négative # fonction zéta # opérateur de transfert # orbite périodique # système d'Anosov # flot hyperbolique

37A05 ; 35A10 ; 37B10 ; 37C10 ; 37C27 ; 37C30 ; 37C35 ; 37C40 ; 37D20 ; 37D35 ; 37D40

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- vi; 313 p.
ISBN 978-0-521-87909-5

Cambridge tracts in mathematics , 0185

Localisation : Collection 1er étage

action de groupe # groupe abélien # rigidité # cocycle # cohomologie des groupes

37-02 ; 37D99 ; 37D30 ; 37D20 ; 57S25 ; 37C15 ; 37C85 ; 37C40 ; 37D25

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- 121 p.
ISBN 978-0-8218-3496-1

University lecture series , 0030

Localisation : Collection 1er étage

construction combinatoire # analyse combinatoire # théorie ergodique # dynamique # système dynamique # approximation # multiplicité spectrale # cohomologie

37A20 ; 37A25 ; 37C40 ; 37D20 ; 37D30

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- vii; 326 p.
ISBN 978-3-319-43058-4

Lecture notes in mathematics , 2164

Localisation : Collection 1er étage

Chaire Jean-Morlet # CIRM # dynamique # théorie ergodique # géométrie différentielle

37C40 ; 37D40 ; 37-06 ; 53-06 ; 37Axx ; 53Cxx

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- 339 p.
ISBN 978-0-8218-4274-4

Fields institute communications , 0051

Localisation : Collection 1er étage

système dynamique # théorie ergodique # ergodicité lisse # système hyperbolique # flots sur surface # méthode quasiconforme # théorie de Teichmüller # foliation # groupe de Kleinian # surface modulaire de Riemann

37C40 ; 37D25 ; 37D30 ; 37E35 ; 37F30 ; 37C85 ; 30F60 ; 30F40 ; 32G15

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- xxvii; 274 p.
ISBN 978-2-85629-916-6

Astérisque , 0415

Localisation : Périodique 1er étage

actions de groupes paraboliques # automorphismes polynomiaux de $\mathbb{C}^{2}$ # Birkhoff # cocycles projectivisés # combinatoire # compacité # courbe analytique réelle # courbes férales # courbes pseudoholomorphiques # décomposition de Thurston-Nielsen # diagramme de cordes # diagramme de Rauzy # diagramme de séparatrices # dimensions # distribution de Cauchy # distribution uniforme # éclatement # ensembles de Cantor réguliers # espaces des modules des différentielles abéliennes # exposants de Lyapunov # graphe distance héréditaire # groupe nilpotent # lemme de fermeture ergodique # mécanique des fluides numérique # mesures invariantes # nombre d'enlacement # nombre de rotation # opérade # Poincaré # point fixe # quasi-périodicité # récurrence par chaînes # revêtement infini cyclique # rotations du cercle # singularité # spectres dynamiques de Markov et Lagrange # surface à petits carreaux # systèmes dynamiques # théorèmes limites "annealed" # théorèmes limites pour les moyennes temporelles # volume de Masur-Veech actions de groupes paraboliques # automorphismes polynomiaux de $\mathbb{C}^{2}$ # Birkhoff # cocycles projectivisés # combinatoire # compacité # courbe analytique réelle # courbes férales # courbes pseudoholomorphiques # décomposition de Thurston-Nielsen # diagramme de cordes # diagramme de Rauzy # diagramme de séparatrices # dimensions # distribution de Cauchy # distribution uniforme # éclatement # ensembles de Cantor réguliers # espaces des ...

05A05 ; 05A16 ; 11J06 ; 20C30 ; 28A78 ; 30F30 ; 30F60 ; 32Q65 ; 34D08 ; 37Bxx ; 37B20 ; 37C40 ; 37C60 ; 37C85 ; 37D20 ; 37D25 ; 37E30 ; 37F10 ; 37F15 ; 37F45 ; 57S25 ; 58F08 ; 76A99 ; 37C55 ; 37D35 ; 53D42

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- xvii; 340 p.
ISBN 978-2-85629-917-3

Astérisque , 0416

Localisation : Périodique 1er étage

accessibilité # application Gevrey # $(C^{0})$-commutativité au sens de Poisson # centralisateurs # changements de temps # complète integrabilité # conditions diophantiennes # coordonnées de Fatou # décroissance des corrélations # déviations des moyennes ergodiques # difféomorphismes analytiques du cercle # dimension centrale # distribution limites # domaine de rotation # dynamique holomorphe # échanges d'intervalle # feuilletage invariant # feuilletages # flots nilpotents de Heisenberg # fonctions génératrices # germes holomorphes de $\mathbb{C}^{2}$ # hamiltoniens # hérissons # homéomorphismes symplectiques # hyperbolicité faible # hyperbolicité partielle # instabilité # linéarisation # mélange # nombre de rotation # pétales invariants # petits diviseurs # point fixe elliptique # points fixes indifférents # renormalisation # renormalisation sectorielle # sommes de Birkhoff # sous-variétés lagrangiennes # symplectomorphisme # système dynamique # théorème de translation plane de Brouwer # théorèmes d’Arnold- Liouville # type Roth # variété centrale # vitesses de mélange accessibilité # application Gevrey # $(C^{0})$-commutativité au sens de Poisson # centralisateurs # changements de temps # complète integrabilité # conditions diophantiennes # coordonnées de Fatou # décroissance des corrélations # déviations des moyennes ergodiques # difféomorphismes analytiques du cercle # dimension centrale # distribution limites # domaine de rotation # dynamique holomorphe # échanges d'intervalle # feuilletage invariant # ...

32A10 ; 37A17 ; 37A25 ; 37A50 ; 37C40 ; 37C75 ; 37D30 ; 37E05 ; 37E30 ; 37F25 ; 37F50 ; 37J50 ; 53D12 ; 60F05 ; 70H20 ; 37D25

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- viii; 155 p.
ISBN 978-1-4704-4215-6

Memoirs of the American Mathematical Society , 1291

Localisation : Collection 1er étage

groupe de Carnot Iwasawa # groupe d'Heisenberg # système de fonctions itérées # condition d'un ensemble ouvert # cartographie conforme # formalisme thermodynamique # formule de Bowen # dimension de Hausdorff # mesure de Hausdorff # mesure de tassement # fraction continue

30L10 ; 53C17 ; 37C40 ; 11J70 ; 28A78 ; 37B10 ; 37C30 ; 37D35 ; 37F35 ; 47H10

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