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

... Lire [+]

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

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 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 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 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

... Lire [+]

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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- xxii; 266 p.
ISBN 978-2-85629-843-5

Astérisque , 0382

Localisation : Périodique 1er étage

forme modulaire de Hilbert # forme modulaire $\rho$-adique # forme modulaire surconvergente # représentation galoisienne # modularité # conjecture d'Artin # conjecture de Fontaine-Mazur

37A20 ; 37D25 ; 37D30 ; 37A50 ; 37C40

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- ix; 165 p.
ISBN 978-2-85629-778-0

Astérisque , 0358

Localisation : Périodique 1er étage

Cocycle abélien # équation cohomologique # invariant d'holonomie # principe d'invariance # cocycle linéaire # théorie de Livsic # exposant de Liapounoff # hyperbolicité partielle # rigidité # cocycle lisse

37A20 ; 37D25 ; 37D30 ; 37A50 ; 37C40

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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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- 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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- 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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- 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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- ix; 277 p.
ISBN 978-0-8218-9853-6

Graduate studies in mathematics , 0148

Localisation : Collection 1er étage

système dynamique # théorie ergodique # exposant de Lyapunov # dynamique topologique # hyperbolicité non-uniforme # flot géodésique

37D25 ; 37C40 ; 37-01

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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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- 151 p.
ISBN 978-0-8218-2921-9

University lecture series , 0023

Localisation : Collection 1er étage

système dynamique # théorie ergodique # théorie ergodique continue # exposant de Lyapunov # système hyperbolique non-uniforme # variété stable # variété locale

37C40 ; 37D25 ; 34D08

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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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