Recurrence near given sets and the complexity of the Casati-Prosen map (Q1776624)

The authors prove a result that gives an estimate on the rate for approaching a generic orbit near a given set. More precisely, they show that the time of first entrance of a generic orbit into some neighborhood of a given set can be estimated from below by the dimension of the invariant measure near the given set. The authors use this result to study certain complexity indicators for individual orbits generated by a simple (two parameter family) discontinuous area-preserving map over the torus.