Genericity along curves and applications
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: MSRI: Simons Auditorium
Birkhoff's ergodicity theorem
37-XX - Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
37D50 - Hyperbolic systems with singularities (billiards, etc.)
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
We will present two results in mathematical physics which can be obtained as applications of a result in homogeneous dynamics. The applications concern the dynamics in a class of pseudo-integrable billiards in ellipses and the behaviour of light rays in arrays of Eaton lenses. They are based on an equidistribution result in the space of affine lattices, that guarantees that typical points on certain curves are Birkhoff generic for the geodesic flow. For the Eaton lenses application we also prove an Oseledets genericity result which generalizes in this set up a recent result by Eskin and Chaika. The talk is based on joint work with Krzysztof Fraczek and Ronggang Shi.
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