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Convergence of moments for Axiom A and non-uniformly hyperbolic flows
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Melbourne, Ian and Torok, Andrei (2012) Convergence of moments for Axiom A and non-uniformly hyperbolic flows. Ergodic Theory and Dynamical Systems, Vol.32 (No.3). pp. 1091-1100. doi:10.1017/S0143385711000174 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S0143385711000174
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: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0143-3857 | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| Volume: | Vol.32 | ||||
| Number: | No.3 | ||||
| Page Range: | pp. 1091-1100 | ||||
| DOI: | 10.1017/S0143385711000174 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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