Title: SPR property and exponential mixing of mmes of interval maps
Abstract: In their recent work, Buzzi, Crovisier, Sarig introduced the notion of Strong Positive Recurrence for diffeomorphisms. They show that these systems enjoy great ergodic properties, including the existence, finiteness and the exponential mixing of measures of maximal entropy.
We follow their line to introduce an analogues notion for maps in dimension 1. The idea involves the symbolic coding of the system, proving entropic continuity of Lyapunov exponents, and using the machinery of topological Markov shifts. As a result, we show exponential mixing of the measures of maximal entropy of these systems.
This consists a series of works, including one joint with Jérôme Buzzi and Dawei Yang, one with Alexandre Delplanque.