Ergodic Theory Dyn. Syst. 32 (2012) 1091-1100
Ian Melbourne and Andrei Török
Abstract
In the paper, we prove convergence of moments of all orders for Axiom A diffeomorphisms and flows. The same results hold for nonuniformly hyperbolic diffeomorphisms and flows modelled by Young towers with superpolynomial tails. For polynomial tails, we prove convergence of moments up to a certain order, and give examples where moments diverge when this order is exceeded.
Nonuniformly hyperbolic systems covered by our result include
Hénon-like attractors, Lorenz attractors, semidispersing billiards,
finite horizon planar periodic Lorentz gases, and Pomeau-Manneville
intermittency maps.