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# Documents  37C05 | enregistrements trouvés : 12

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## Perturbative techniques of the dynamics in the $C^1$-topology Crovisier, Sylvain | CIRM H

Post-edited

Research talks;Dynamical Systems and Ordinary Differential Equations

These lectures will address the dynamics of vector fields or diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb while controlling the dynamics: closing and connection of orbits, perturbation of the tangent dynamics... We derive various applications to the description of $C^1$-generic diffeomorphisms. These lectures will address the dynamics of vector fields or diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb ...

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## Smooth parametrizations in analysis, dynamics, and diophantine geometry Yomdin, Yosef | CIRM H

Multi angle

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

Smooth parametrization consists in a subdivision of mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the talk is to provide a short overview of some results and open problems on smooth parametrization and its applications in several apparently separated domains: Smooth Dynamics, Diophantine Geometry, and Approximation Theory. The structure of the results, open problems, and conjectures in each of these domains shows in many cases a remarkable similarity, which I’ll try to stress. Sometimes this similarity can be easily explained, sometimes the reasons remain somewhat obscure, and it motivates some natural questions discussed in the talk. I plan to present also some new results, connecting smooth parametrization with “Remez-type” (or “Norming”) inequalities for polynomials restricted to analytic varieties. Smooth parametrization consists in a subdivision of mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the talk is to provide a short overview of some results and open problems on smooth parametrization and its applications in several apparently separated domains: Smooth Dynamics, Diophantine Geometry, and Approximation ...

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

Multi angle

Research School;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 ...

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

Multi angle

Research School;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 ...

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

Multi angle

Research School;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 ...

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## Shadowing in dynamical systems Pilyugin, Sergei Yu. | Springer 1999

Ouvrage

- 271 p.
ISBN 978-3-540-66299-0

Lecture notes in mathematics , 1706

Localisation : Collection 1er étage

système dynamique # Shadowing # équation différentielle # EDP # système hamiltonien # système hyperbolique # orbite # ensemble invariant # difféomorphisme # stabilité structurelle # stabilité # application numérique # exponentielle de Lyapunov

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## Geometric methods for discrete dynamical systems Easton, Robert W. | Oxford University Press 1998

Ouvrage

- 157 p.
ISBN 978-0-19-508545-7

Oxford engineering science series , 0050

Localisation : Ouvrage RdC (EAST)

géométrie # système dynamique discret # point fixe hyperbolique # géométrie symplectique # mesure invariante # exercice # théorie des indexes # index de Conley

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## Dynamical properties of diffeomorphisms of the annulus and of the Torus Le Calvez, Patrice | American Mathematical Society 2000

Ouvrage

- 105 p.
ISBN 978-0-8218-1943-2

SMF/AMS texts and monographs , 0004

Localisation : Collection 1er étage

anneau # Tore # difféomorphisme # système dynamique dérivable # application

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## Nonlinear dynamics and evolution equations Brunner, Hermann ; Zhao, Xiao-Qiang ; Zou, Xingfu | American Mathematical Society 2006

Ouvrage

- 311 p.
ISBN 978-0-8218-3721-4

Fields institute communications , 0048

Localisation : Collection 1er étage

équation différentielle # système dynamique différentiel # dynamique # comportement asymptotique des solutions # problème de valeures limites # application lisse # flux monotone # perturbations variétés de poisson # dynamique des populations # épidémiologie

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## Fine structures of hyperbolic diffeomorphisms Pinto, Alberto A. ; Rand, David A. ; Ferreira, Flavio | Springer 2009

Ouvrage

- 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

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## Perturbation de la dynamique de difféomorphismes en topologie C^1 Crovisier, Sylvain | Société Mathématique de France 2013

Ouvrage

- vii; 164 p.
ISBN 978-2-85629-764-3

Astérisque , 0354

Localisation : Périodique 1er étage

Difféomorphisme # généricité # lemme de fermeture # lemme de connection # classe homocline # pseudo-orbite # dynamique hyperbolique # tangence homocline # cycle hétérodimensionnel # hyperbolicité partielle # décomposition dominée # pistage # variété invariante # modèle central # centralisateur

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## Sovremennye problemy matematiki. Fundamental'nye napravleniya. Tom 1 [Les problèmes actuels des mathématiques. les directions fondamentales] :dinamicheskie sistemy. 1 [les systèmes dynamiques. 1] Gamkrelidze, R. | VINITI 1985

Ouvrage

- 244 p.
ISBN

Itogi Nauki i Tekhniki

Localisation : Fonds Russe réserve

équation différentielle # points singulier # cycle limite # système dynamique lisse # système de Morse-Smale # flux des surfaces

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