Statistics of Poincaré recurrences for a class of smooth circle maps (Q1771755)

The paper is a predominantly numerical investigation of the statistics of return times for a class of circle maps given as smooth perturbations of uniform rotations. It is found that in the sub-critical and critical regions there are at most three return times (provided that the rotation number is sufficiently irrational), while in the strongly super-critical region the return times are seen to typically decay exponentially with decay rate 1.