a1 Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK (email: firstname.lastname@example.org)
a2 Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (email: email@example.com)
a3 Institute of Mathematics of the Romanian Academy, PO Box 1-764, RO-70700 Bucharest, Romania
In the paper, we prove convergence of moments of all orders for Axiom A diffeomorphisms and flows. The same results hold for non-uniformly 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. Non-uniformly 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.
(Received October 12 2010)
(Revised March 01 2011)
(Online publication June 10 2011)