'Hyperbolic Dynamical Systems and Related Topics' (2013-14)

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source: Centre International de Rencontres Mathématiques    2015年8月6日
Jean-Morlet Chair - Research Talks - Hasselblatt/Troubetzkoy
Semester on 'Hyperbolic Dynamical Systems and Related Topics'
November 2013 - April 2014
General themes
The scientific focus of this Chair was on hyperbolic dynamical systems and related topics. This is a broad and active area of research throughout the world which is on one hand at the core of Boris Hasselblatt's research record and interests and on the other hand well represented in the Marseille region.
Moreover, hyperbolic dynamics has broad interactions with numerous other areas of dynamical systems and mathematics: partial differential equations viewed as infinite-dimensional dynamical systems, celestial mechanics, statistical mechanics, geometry (of nonpositively curved manifolds),Teichmüller theory, topology, to name a few.
In addition, hyperbolic dynamics is important to a broad range of subjects in applied mathematics.

Pierre Dehornoy: Wich geodesic flows are left-handed? 1:05:25
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Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows are good candidates. In this conference we determine on which hyperbolic orbifolds is the geodesic flow left-handed: the answer is that yes if the surface is a sphere with three cone points, and no otherwise.
Recording during the thematic meeting: "Jean Morlet Chair : Young mathematicians in dynamical systems" the November 27, 2013 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Barbara Schapira: Horocyclic flows on hyperbolic surfaces - Part I 1:34:13
Federico Rodriguez Hertz: Rigidity of hyperbolic higher rank lattice actions 1:00:13
Mark Pollicott: Dynamical definitions of the Weil-Petersson metric on moduli space 47:36
DamienThomine: Precise statistical properties of the geodesic flow on periodic hyperbolic manifolds 55:09
Masato Tsujii: Spectrum of geodesic flow on negatively curved manifold 56:43
Mike Hochman: Dimension of self-similar measures via additive combinatorics 53:08

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