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Documents  Forni, Giovanni | enregistrements trouvés : 3

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Research talks;Dynamical Systems and Ordinary Differential Equations

We prove a couple of general conditional convergence results on ergodic averages for horocycle and geodesic subgroups of any continuous $SL(2,\mathbb{R})$- action on a locally compact space. These results are motivated by theorems of Eskin, Mirzakhani and Mohammadi on the $SL(2,\mathbb{R})$-action on the moduli space of Abelian differentials. By our argument we can derive from these theorems an improved version of the “weak convergence” of push-forwards of horocycle measures under the geodesic flow and a new short proof of a theorem of Chaika and Eskin on Birkhoff genericity in almost all directions for the Teichmüller geodesic flow. We prove a couple of general conditional convergence results on ergodic averages for horocycle and geodesic subgroups of any continuous $SL(2,\mathbb{R})$- action on a locally compact space. These results are motivated by theorems of Eskin, Mirzakhani and Mohammadi on the $SL(2,\mathbb{R})$-action on the moduli space of Abelian differentials. By our argument we can derive from these theorems an improved version of the “weak convergence” of ...

37D40 ; 37C40 ; 37A17

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Research talks;Dynamical Systems and Ordinary Differential Equations;Algebraic and Complex Geometry

We will present a geometric criterion for the ergodicity of the billiard flow in a polygon with non-rational angles and discuss its application to the Diophantine case.

37D40 ; 37D50 ; 30F10 ; 30F60 ; 32G15

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- 339 p.
ISBN 978-0-8218-4274-4

Fields institute communications , 0051

Localisation : Collection 1er étage

système dynamique # théorie ergodique # ergodicité lisse # système hyperbolique # flots sur surface # méthode quasiconforme # théorie de Teichmüller # foliation # groupe de Kleinian # surface modulaire de Riemann

37C40 ; 37D25 ; 37D30 ; 37E35 ; 37F30 ; 37C85 ; 30F60 ; 30F40 ; 32G15

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