The spectrum of Poincare recurrence
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AbstractWe investigate the relationship between Poincare recurrence and topological entropy of a dynamical system (X, f). For 0 <= alpha <= beta <= infinity, let D(alpha, beta) be the set of x with lower and upper recurrence rates a and P, respectively. Under the assumptions that the system is not minimal and that the map f is positively expansive and satisfies the specification condition, we show that for any open subset empty set not equal U subset of X, D(alpha, beta) boolean AND U has the full topological entropy of X. This extends a result of Feng and Wu [The Hausdorff dimension of recurrence sets in symbolic spaces. Nonlinearity 14 (2001), 81-85] for symbolic spaces.
All Author(s) ListLau KS, Shu L
Journal nameErgodic Theory and Dynamical Systems
Year2008
Month12
Day1
Volume Number28
PublisherCAMBRIDGE UNIV PRESS
Pages1917 - 1943
ISSN0143-3857
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesMathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2021-05-04 at 00:25