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

Melbourne, I and Toeroek, A (2012) Convergence of moments for Axiom A and non-uniformly hyperbolic flows ERGODIC THEORY AND DYNAMICAL SYSTEMS, 32 (3). 1091 - 1100. ISSN 0143-3857

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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.

Item Type: Article
Additional Information: Copyright 2012 Cambridge University Press. Reproduced with permission.
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 26 Jul 2012 12:15
Last Modified: 23 Sep 2013 19:31
URI: http://epubs.surrey.ac.uk/id/eprint/649009

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