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Documents  Schapira, Barbara | enregistrements trouvés : 6

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Research talks;Dynamical Systems and Ordinary Differential Equations

I will present results on the dynamics of horocyclic flows on the unit tangent bundle of hyperbolic surfaces, density and equidistribution properties in particular. I will focus on infinite volume hyperbolic surfaces. My aim is to show how these properties are related to dynamical properties of geodesic flows, as product structure, ergodicity, mixing, ...

37D40

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Research talks;Dynamical Systems and Ordinary Differential Equations;Topology

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.
dynamical system - geodesic flow - knot - periodic orbit - global section - linking number - fibered knot
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 ...

37C27 ; 37C15 ; 37C10 ; 57M25

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Research talks;Dynamical Systems and Ordinary Differential Equations

37D40 ; 37A50 ; 37D10

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Research schools;Dynamical Systems and Ordinary Differential Equations

We will discuss old and recent results on topological and measurable dynamics of diagonal and unipotent flows on frame bundles and unit tangent bundles over hyperbolic manifolds. The first lectures will be a good introduction to the subject for young researchers.

37D40 ; 37A17 ; 37A25

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- 270 p.
ISBN 978-2-940264-08-7

Monographie de l'Enseignement Mathématique , 0041

Localisation : Ouvrage RdC (THEO)

système dynamique # action de groupes # théorème ergodique # groupe moyennable

37-02 ; 37B05 ; 37A30

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- viii; 281 p.
ISBN 978-2-85629-818-3

Astérisque , 0373

Localisation : Périodique 1er étage

flot géodésique # courbure négative # état de Gibbs # période # dénombrement d'orbites # densité de Patterson # pression # principe variationnel # foliation instable et forte

37D35 ; 53D25 ; 37D40 ; 37A25 ; 37C35 ; 53C12

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