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Unique equilibrium states for geodesic flows over manifolds without focal-points

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Auteurs : Kao, Lien-Yung (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : 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.

Keywords : maniflods without focal-points; geodesic flows; equilibrium state

Codes MSC :
37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D35 - Thermodynamic formalism, variational principles, equilibrium states
 37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
    Informations sur la Vidéo

    Réalisateur : Recanzone, Luca
    Langue : Anglais
    Date de publication : 31/07/2019
    Date de captation : 01/07/2019
    Sous collection : Research School
    arXiv category : Dynamical Systems ; Differential Geometry
    Domaine : Dynamical Systems & ODE ; Geometry
    Format : MP4 (.mp4) - HD
    Durée : 00:48:52
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-07-01_Kao.mp4
Informations sur la Rencontre

Nom de la rencontre : 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
Organisateurs de la rencontre : Pollicott, Mark ; Vaienti, Sandro
Dates : 01/07/2019 - 05/07/2019
Année de la rencontre : 2019
URL Congrès : https://www.chairejeanmorlet.com/2110.html

Données de citation

DOI : 10.24350/CIRM.V.19541703
Citer cette vidéo: Kao, Lien-Yung (2019). Unique equilibrium states for geodesic flows over manifolds without focal-points. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19541703
URI : http://dx.doi.org/10.24350/CIRM.V.19541703

Voir aussi

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