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Entropy and growth of periodic orbits for Anosov flows and their covers

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Authors : Sharp, Richard (Author of the conference)
CIRM (Publisher )

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Abstract : In this talk, we will discuss various growth rates associated to Anosov flows and their covers. The topological entropy of an Anosov flow on a compact manifold is realised as the exponential growth rate of its periodic orbits. If we pass to a regular cover of the manifold then we can consider a corresponding growth rate for the lifted flow. This growth is bounded above by the topological entropy but if the cover is infinite then the growth rate may be strictly smaller. For abelian covers, this phenomenon admits a precise description in terms of a variational principle. More recent work, joint with Rhiannon Dougall, considers more general infinite covers.

Keywords : periodic orbits; Anosov flows; topological entropy; regular covers; amenable groups

MSC Codes :
37B40 - Topological entropy
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D35 - Thermodynamic formalism, variational principles, equilibrium states
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 31/07/2019
    Conference Date : 01/07/2019
    Subseries : Research School
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Video Time : 00:57:50
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-07-01_Sharp.mp4

Information on the Event

Event Title : Jean-Morlet Chair 2019 - Research School: Thermodynamic Formalism: Modern Techniques in Smooth Ergodic Theory / Chaire Jean-Morlet 2019 - Ecole : Formalisme thermodynamique : techniques modernes en théorie ergodique
Event Organizers : Pollicott, Mark ; Vaienti, Sandro
Dates : 01/07/2019 - 05/07/2019
Event Year : 2019
Event URL : https://www.chairejeanmorlet.com/2110.html

Citation Data

DOI : 10.24350/CIRM.V.19542003
Cite this video as: Sharp, Richard (2019). Entropy and growth of periodic orbits for Anosov flows and their covers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19542003
URI : http://dx.doi.org/10.24350/CIRM.V.19542003

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