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Poincaré recurrence for observations

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 relatively to the push-forward are equal.
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https://hal.univ-brest.fr/hal-00293637
Contributor : Benoit Saussol <>
Submitted on : Monday, July 7, 2008 - 10:58:50 AM
Last modification on : Wednesday, April 1, 2020 - 1:57:16 AM
Long-term archiving on: : Friday, May 28, 2010 - 9:31:11 PM

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  • HAL Id : hal-00293637, version 1
  • ARXIV : 0807.0970

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Jerôme Rousseau, Benoit Saussol. Poincaré recurrence for observations. 2008. ⟨hal-00293637⟩

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