Optimal bounds on correlation decay rates for nonuniform hyperbolic systems

Sandro Vaienti (1, 2) , Hong-Kun Zhang (3)

1 CPT - Ex E7 Systèmes dynamiques et théorie ergodique
2 CPT - Centre de Physique Théorique - UMR 7332
3 Department of Math. and Stat.,

We investigate the decay rates of correlations for nonuniformly hy-perbolic systems with or without singularities, on piecewise Hölder ob-servables. By constructing a new scheme of coupling methods using the probability renewal theory, we obtain the optimal bounds for decay rates of correlations for a large class of observables. Our results apply to rather general hyperbolic systems, including Bunimovich Stadia, Bunimovich billiards , semidispersing billiards on a rectangle and billiards with cusps, and to a wide class of nonuniformly hyperbolic maps.

Domaines: Systèmes dynamiques [math.DS]

Sandro Vaienti, Hong-Kun Zhang. Optimal bounds on correlation decay rates for nonuniform hyperbolic systems. 2016. ⟨hal-01312743⟩