CIRM - Videos & books Library - A model-theoretic analysis of geodesic equations in negative curvature

Virtualconference

Auteurs : Jaoui, Rémi (Auteur de la conférence)
CIRM (Editeur )

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Résumé : To any algebraic differential equation, one can associate a first-order structure which encodes some of the properties of algebraic integrability and of algebraic independence of its solutions.To describe the structure associated to a given algebraic (nonlinear) differential equation (E), typical questions are:- Is it possible to express the general solutions of (E) from successive resolutions of linear differential equations?- Is it possible to express the general solutions of (E) from successive resolutions of algebraic differential equations of lower order than (E)?- Given distinct initial conditions for (E), under which conditions are the solutions associated to these initial conditions algebraically independent?In my talk, I will discuss in this setting one of the first examples of non-completely integrable Hamiltonian systems: the geodesic motion on an algebraically presented compact Riemannian surface with negative curvature. I will explain a qualitative model-theoretic description of the associated structure based on the global hyperbolic dynamical properties identified by Anosov in the 70's for the geodesic motion in negative curvature.

Codes MSC :
12H05 - Differential algebra
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53C22 - Geodesics [See also 58E10]
53D25 - Geodesic flows

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-05-25_Jaoui.mp4

Informations sur la Rencontre

Nom de la Rencontre : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages
Organisateurs de la Rencontre : Druel, Stéphane ; Pereira, Jorge Vitório ; Rousseau, Erwan
Dates : 18/05/2020 - 22/05/2020
Année de la rencontre : 2020
URL de la Rencontre : https://www.chairejeanmorlet.com/2251.html

Données de citation

DOI : 10.24350/CIRM.V.19638203
Citer cette vidéo: Jaoui, Rémi (2020). A model-theoretic analysis of geodesic equations in negative curvature. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19638203
URI : http://dx.doi.org/10.24350/CIRM.V.19638203

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