Return time entropies for a class of circle homeomorphisms

Abstract

Poincar ́e recurrence for a class of circle maps is used to study the properties of the corresponding invariant measures. In the subcritical case, when the map is a diffeomorphism, the return time measure is smooth, and in the critical case, when the map is only a homeomorphism, the measure is only continuous. Furthermore, in the considered class of critical maps the behaviour of the return time entropy depends only on the tail in the continued fraction expansion of the rotation number.