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Convergence of moments for Axiom A and non-uniformly hyperbolic flows

Published online by Cambridge University Press:  10 June 2011

IAN MELBOURNE  and
ANDREI TÖRÖK
IAN MELBOURNE
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK (email: ism@math.uh.edu)
ANDREI TÖRÖK
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (email: torok@math.uh.edu) Institute of Mathematics of the Romanian Academy, PO Box 1-764, RO-70700 Bucharest, Romania
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 3 , June 2012 , pp. 1091 - 1100
Copyright
Copyright © Cambridge University Press 2011

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