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Spring Topology and Dynamics Conference 2006
March 23-25, 2006
University of North Carolina at Greensboro
Greensboro, NC, USA

Organizers
Gregory Bell, Alexander Chigogidze, Paul Duvall, Jan Rychtar, Jerry Vaughan

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Rotation sets of billiards with one obstacle
by
Michal Misiurewicz
Indiana University - Purdue University Indianapolis
Coauthors: Alexander Blokh (University of Alabama in Birmingham), Nandor Simanyi (University of Alabama in Birmingham)

We investigate billiards on the m-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. The rotation set of a dynamical system consists of all limits of averages over the trajectories of a certain displacement function. In the first case the displacement function measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets.

Date received: January 30, 2006

Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqs-14.