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Audiovisual Mathematics Library

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Multi angle

Authors : Burguet, David (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

Keywords : entropy; smooth parametrizations

MSC Codes :
37C05 - Smooth mappings and diffeomorphisms
37C40 - Smooth ergodic theory, invariant measures
37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)

Additional resources :
https://www.cirm-math.fr/RepOrga/2264/Slides/Burguet-3-slides.pdf

Information on the Video

Film maker :

Hennenfent, Guillaume

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Download :

https://videos.cirm-math.fr/2019-05-22_Burguet_part3.mp4

Information on the Event

Event Title : Dynamique au-delà de l'hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity
Event Organizers : Bonatti, Christian ; Buzzi, Jérôme ; Crovisier, Sylvain ; Gan, Shaobo ; Pacifico, Maria José
Dates : 13/05/2019 - 24/05/2019
Event Year : 2019
Event URL : https://conferences.cirm-math.fr/1947.html

Citation Data

DOI : 10.24350/CIRM.V.19527003
Cite this video as: Burguet, David (2019). Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19527003
URI : http://dx.doi.org/10.24350/CIRM.V.19527003

See Also

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[Multi angle] Ergodic optimization - lecture 2 / Author of the conference Contreras, Gonzalo.
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[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 2 / Author of the conference Burguet, David.
[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 1 / Author of the conference Burguet, David.
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[Multi angle] Transfer operators for Sinai billiards - lecture 2 / Author of the conference Baladi, Viviane.
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