Dynamique au-delà de l’hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity

Collection Dynamique au-delà de l’hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity

Organizer(s) Bonatti, Christian ; Buzzi, Jérôme ; Crovisier, Sylvain ; Gan, Shaobo ; Pacifico, Maria José

Date(s) 13/05/2019 - 24/05/2019

linked URL https://conferences.cirm-math.fr/1947.html

00:00:00 / 00:00:00

22 32

Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 2

By David Burguet

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.

Information about the video

Date of recording 21/05/2019
Date of publication 11/06/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.19526903
Cite this video Burguet, David (21/05/2019). Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19526903
URL https://dx.doi.org/10.24350/CIRM.V.19526903

Domain(s)

Dynamical Systems

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2264/Slides/Burguet-2-slides.pdf

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