Recurrence near given sets and the complexity of the Casati-Prosen map

摘要

We prove a quantitative recurrence result which allow to estimate the speed of approaching of a generic orbit to the discontinuities of a map. This result is applied to the study of complexity indicators for individual orbits generated by a certain zero-entropy discontinuous maps which are related to polygonal billiards and quantum chaos. (C) 2004 Elsevier Ltd. All rights reserved.