Genericity along curves and applications
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: SLMath: Eisenbud Auditorium
billiards dynamics
elliptical billiards
integrable systems
ergodic flow
bounded trajectory
Birkhoff's ergodicity theorem
35Q60 - PDEs in connection with optics and electromagnetic theory
35Q79 - PDEs in connection with classical thermodynamics and heat transfer
35Q81 - PDEs in connection with semiconductor devices {For statistical mechanics, see 82D37}
37-04 - Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory
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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.
Ulcigrai Notes
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