m
• E

F Nous contacter

0

# Documents  37D25 | enregistrements trouvés : 34

O

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Geometric and probabilistic structures in dynamics:workshop on dynamical systems and related topics in honor of Michael Brin on the occasion of his 60th birthdayCollege Park # march 15-18, 2008 Burns, Keith ; Dolgopyat, Dmitry ; Pesin, Yakov | American Mathematical Society 2008

Congrès

- xv; 340 p.
ISBN 978-0-8218-4286-7

Contemporary mathematics , 0469

Localisation : Collection 1er étage

système dynamique # méthode probabiliste # géométrie riemannienne # biologie # dynamique symbolique # dynamique stochastique # dynamique aléatoire

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## ​Limit theorems for almost Anosov flows Terhesiu, Dalia | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

​An almost Anosov flow is a flow having continuous flow-invariant splitting of the tangent bundle with exponential expansion/contraction in the unstable/stable direction, except for a finite number (in our case a single) periodic orbits. Roughly, almost Anosov flows are perturbed Anosov flows, where the perturbation is local around these periodic orbits, making them neutral. For this type of flows, we obtain limit theorems (stable, standard and non-standard CLT) for a large class of (unbounded) observables. I will present these results stressing on the method of proof. This is joint work with H. Bruin and M. Todd. ​An almost Anosov flow is a flow having continuous flow-invariant splitting of the tangent bundle with exponential expansion/contraction in the unstable/stable direction, except for a finite number (in our case a single) periodic orbits. Roughly, almost Anosov flows are perturbed Anosov flows, where the perturbation is local around these periodic orbits, making them neutral. For this type of flows, we obtain limit theorems (stable, standard and ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## ​Levy diffusion of dispersing billiards with flat points Zhang, Hong-Kun | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

​We investigate the diffusion and statistical properties of Lorentz gas with cusps at flat points. This is a modification of dispersing billiards with cusps. The decay rates are proven to depend on the degree of the flat points, which varies from $n^{-a}$, for $a\in (0,\infty)$. The stochastic processes driven by these systems enjoy stable law and have super-diffusion driven by Lévy process. This is a joint work with Paul Jung and Françoise Pène. ​We investigate the diffusion and statistical properties of Lorentz gas with cusps at flat points. This is a modification of dispersing billiards with cusps. The decay rates are proven to depend on the degree of the flat points, which varies from $n^{-a}$, for $a\in (0,\infty)$. The stochastic processes driven by these systems enjoy stable law and have super-diffusion driven by Lévy process. This is a joint work with Paul Jung and Françoise ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Fast slow systems with chaotic noise Kelly, David | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

It has long been observed that multi-scale systems, particularly those in climatology, exhibit behavior typical of stochastic models, most notably in the unpredictability and statistical variability of events. This is often in spite of the fact that the underlying physical model is completely deterministic. One possible explanation for this stochastic behavior is deterministic chaotic effects. In fact, it has been well established that the statistical properties of chaotic systems can be well approximated by stochastic differential equations. In this talk, we focus on fast-slow ODEs, where the fast, chaotic variables are fed into the slow variables to yield a diffusion approximation. In particular we focus on the case where the chaotic noise is multidimensional and multiplicative. The tools from rough path theory prove useful in this difficult setting. It has long been observed that multi-scale systems, particularly those in climatology, exhibit behavior typical of stochastic models, most notably in the unpredictability and statistical variability of events. This is often in spite of the fact that the underlying physical model is completely deterministic. One possible explanation for this stochastic behavior is deterministic chaotic effects. In fact, it has been well established that the ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## On the algebraic hull of the Kontsevich-Zorich cocycle and applications to finiteness theorems Eskin, Alex | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations;Algebraic and Complex Geometry;Topology

We give a necessary and sufficient condition for the existence of infinitely many non-arithmetic Teichmuller curves in a stratum of abelian differentials. This is joint work with Simion Filip and Alex Wright.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Mixing and rates of mixing for infinite measure flows Melbourne, Ian | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations

We obtain results on mixing and rates of mixing for infinite measure semiflows and flows. The results on rates of mixing rely on operator renewal theory and a Dolgopyat-type estimate. The results on mixing hold more generally and are based on a deterministic (ie non iid) version of Erickson's continuous time strong renewal theorem.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Beyond Bowen specification property - lecture 1 Thompson, Daniel J. | CIRM H

Multi angle

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, ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Beyond Bowen specification property - lecture 2 Thompson, Daniel J. | CIRM H

Multi angle

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, ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Beyond Bowen specification property - lecture 3 Thompson, Daniel J. | CIRM H

Multi angle

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, ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 1 Burguet, David | CIRM H

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 2 Burguet, David | CIRM H

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 3 Burguet, David | CIRM H

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## A brief introduction to concentration inequalities Chazottes, Jean-René | CIRM H

Multi angle

Research schools;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

$Let (X,T)$ be a dynamical system preserving a probability measure $\mu$. A concentration inequality quantifies how small is the probability for $F(x,Tx,\ldots,T^{n-1}x)$ to deviate from $\int F(x,Tx,\ldots,T^{n-1}x) \mathrm{d}\mu(x)$ by an given amount $u$, where $F:X^n\to\mathbb{R}$ is supposed to be separately Lipschitz. The bound on that probability involves a constant $C$ depending only on the dynamical system (thus independent of $n$), and $\sum_{i=0}^{n-1} \mathrm{Lip}_i(F)^2$. In the best situation, the bound is $\exp(-C u^2/\sum_{i=0}^{n-1} \mathrm{Lip}_i(F)^2)$.
After explaining how to get such a bound for independent random variables, I will show how to prove it for a Gibbs measure on a shift of finite type with a Lipschitz potential, and present examples of functions $F$ to which one can apply the inequality. Finally, I will survey some results obtained for nonuniformly hyperbolic systems modeled by Young towers.
$Let (X,T)$ be a dynamical system preserving a probability measure $\mu$. A concentration inequality quantifies how small is the probability for $F(x,Tx,\ldots,T^{n-1}x)$ to deviate from $\int F(x,Tx,\ldots,T^{n-1}x) \mathrm{d}\mu(x)$ by an given amount $u$, where $F:X^n\to\mathbb{R}$ is supposed to be separately Lipschitz. The bound on that probability involves a constant $C$ depending only on the dynamical system (thus independent of $n$), ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Unique equilibrium states for geodesic flows over manifolds without focal-points Kao, Lien-Yung | CIRM H

Multi angle

Research schools;Dynamical Systems and Ordinary Differential Equations;Geometry

We study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class of potentials having unique equilibrium states, including scalar multiples of the geometric potential, provided the scalar is less than 1. Moreover, we discuss ergodic properties of these unique equilibrium states. We show these unique equilibrium states are Bernoulli, and weighted regular periodic orbits are equidistributed relative to these unique equilibrium states. We study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class of potentials having unique equilibrium states, including scalar multiples of the geometric potential, provided the scalar is less than 1. Moreover, we discuss ergodic properties of these unique equilibrium states. We show these unique equilibrium states are Bernoulli, and weighted ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Lyapunov exponents and smooth ergodic theory Barreira, Luis ; Pesin, Yakov B. | American Mathematical Society 2002

Ouvrage

- 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

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Mathematical theory of nonequilibrium steady states :on the frontier of probability and dynamical systems Jiang, D. Q. ; Qian, Min ; Qian, M. P. | Springer 2004

Ouvrage

- 280 p.
ISBN 978-3-540-20611-8

Lecture notes in mathematics , 1833

Localisation : Collection 1er étage

physique statistique # production d'entropie # irréversibilité # équilibre # chaîne de Markov # processus de diffusion # système dynamique hyperbolique # fluctuation de Gallavotti-Cohen

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Lectures on partial hyperbolicity and stable ergodicity Pesin, Yakov | European Mathematical Society 2004

Ouvrage

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

Localisation : Ouvrage RdC (PESI)

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

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Chaotic billiards Chernov, Nokolai ; Markarian, Roberto | American Mathematical Society 2006

Ouvrage

- 316 p.
ISBN 978-0-8218-4096-2

Mathematical surveys and monographs , 0127

Localisation : Collection 1er étage

dynamique # système dynamique # comportement chaotique des systèmes # théorie ergodique # théorie de la mesure # probabilités billiards # système hyperbolique non-uniforme # équilibre # exposant de Lyapunov # billiard de Burnimovich

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## The mathematical foundations of mixing :the linked twist map as a paradigm in applications micro to macro, fluids to solids Sturman, Rob ; Ottino, Julio M. ; Wiggins, Stephen | Cambridge University Press 2006

Ouvrage

- 281 p.
ISBN 978-0-521-86813-6

Cambridge monographs on applied and computational mathematics , 0022

Localisation : Ouvrage RdC (STUR)

application dérivant de la verticlae # système dynamique # mélange # hiérarchie ergodique # ergodicité # propriété de Bernouilli # exposant de Lyapunov # hyperbolicité # torus # fer cheval # biologie

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Nonuniform hyperbolicity :dynamics of systems with nonzero Lyapunov exponents Barreira, Luis ; Pesin, Yakov | Cambridge University Press 2007

Ouvrage

- 513 p.
ISBN 978-0-521-83258-8

Encyclopedia of mathematics and its applications , 0115

Localisation : Collection 1er étage;Réserve

système dynamique # comportement hyperbolique # théorie ergodique # système hyperbolique non uniforme

#### Filtrer

##### Codes MSC

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z