Mats Bylund: Critical recurrence in the real quadratic family

Abstract:

The (real) quadratic family is one of the most well-studied families of dynamical systems, and has served as a representative model of chaotic dynamics for the last three decades. By works of Jakobson and Benedicks--Carleson, and later by Graczyk--Swiatek and Lyubich (to name only a fraction of names), this family of dynamical systems is now very well understood. In this talk I will discuss recurrence, and present a result which completes earlier estimates by Avila--Moreira regarding the rate of recurrence for the critical point to itself for typical non-regular (stochastic, Collet--Eckmann) real quadratic maps.