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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Poincaré recurrence for observations


Authors: Jérôme Rousseau and Benoît Saussol
Journal: Trans. Amer. Math. Soc. 362 (2010), 5845-5859
MSC (2010): Primary 37C45, 37B20; Secondary 37A25, 37DXX, 37M25
Published electronically: June 10, 2010
MathSciNet review: 2661498
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05078-0
PII: S 0002-9947(2010)05078-0
Keywords: Poincaré recurrence, dimension theory
Received by editor(s): July 7, 2008
Published electronically: June 10, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.