Rotation sets of billiards with one obstacle

Details Rotation sets of billiards with one obstacle Rotation sets of billiards with one obstacle

2005-08-16

arxiv.org/abs/math/0508300v1

Commun. Math. Phys. Vol. 266. No. 1 (2006), pp. 239-265

Mathematics

Dynamical Systems

Scientific paper

10.1007/s00220-006-0014-4

We investigate the rotation sets of billiards on the $m$-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, 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.

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