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Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors

  • We study Poincare recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is no longer supported solely by unstable periodic orbits of finite length inside it, but also by other special recurrent trajectories, located outside that region. The presence of the latter leads to a deviation of the distribution of the Poincare first return times from a Poissonian. Consequently, by taking into account the contribution of these special recurrent trajectories, a corrected estimate of the measure is obtained. This has wide experimental implications, as in the laboratory all returns can exclusively be observed for regions of finite size, and only unstable periodic orbits of finite length can be detected

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Metadaten
Author:Murilo S. Baptista, Suso Kraut, Celso Grebogi
ISSN:0031-9007
Document Type:Article
Language:English
Year of first Publication:2005
Year of Completion:2005
Release Date:2017/03/24
Source:Physical Review Letters. - ISSN 0031-9007. - 95 (2005), 9, S. 4
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik