Jérôme Buzzi (CNRS, Laboratoire de Mathématiques d’Orsay)
Santiago Martinchinch introduced Discretized Anosov flows, a large class of partially hyperbolic diffeomorphisms that includes deformations of time-one maps of transitive Anosov flows. Under an assumption of irreducibility, we establish the following dichotomy
– either there are exactly two ergodic measures maximizing the entropy (or MMEs);
– or there is a unique MME with zero center exponent.
The hyperbolic case is open and dense and implies that the MMEs are Bernoulli and exponentially mixing (they satisfy Strong Positive Recurrence).
This is a joint work in progress with Sylvain CROVISIER, Mauricio POLETTI, and Ali TAHZIBI.