Quantitative Shrinking Target Properties for rotations, interval exchanges and billiards in rational polygons

Details Quantitative Shrinking Target Properties for rotations, interval exchanges and billiards in rational polygons Quantitative Shrinking Target Properties for rotations, interval exchanges and billiards in rational polygons

2012-01-04

arxiv.org/abs/1201.0941v1

Mathematics

Dynamical Systems

Scientific paper

This paper presents quantitative shrinking target results for rotations and
then extends them to flows on flat surfaces and particularly billiards in
rational polygons. To do this a quantitative version of a unique ergodicity
criterion of Boshernitzan is established. This is equivalent to a quantitative
version of Masur's criterion.

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