Poincaré recurrence for observations
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- by Jérôme Rousseau and Benoît Saussol PDF
- Trans. Amer. Math. Soc. 362 (2010), 5845-5859 Request permission
Abstract:
A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan’s work, for a measure preserving system we study Poincaré recurrence for the observation. The link between the return time for the observation and the Hausdorff dimension of the image of the invariant measure is considered. We prove that when the decay of correlations is super polynomial, the recurrence rates for the observations and the pointwise dimensions relative to the push-forward are equal.References
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Additional Information
- Jérôme Rousseau
- Affiliation: Université Européenne de Bretagne, Université de Brest, Laboratoire de Mathéma- tiques UMR CNRS 6205, 6 avenue Victor le Gorgeu, CS93837, F-29238 Brest Cedex 3 France
- Email: jerome.rousseau@univ-brest.fr
- Benoît Saussol
- Affiliation: Université Européenne de Bretagne, Université de Brest, Laboratoire de Mathéma- tiques UMR CNRS 6205, 6 avenue Victor le Gorgeu, CS93837, F-29238 Brest Cedex 3 France
- Email: benoit.saussol@univ-brest.fr
- Received by editor(s): July 7, 2008
- Published electronically: June 10, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 5845-5859
- MSC (2010): Primary 37C45, 37B20; Secondary 37A25, 37DXX, 37M25
- DOI: https://doi.org/10.1090/S0002-9947-2010-05078-0
- MathSciNet review: 2661498