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The spectrum of Poincaré recurrence

Published online by Cambridge University Press:  15 September 2008

KA-SING LAU  and
LIN SHU
KA-SING LAU
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong (email: [email protected])
LIN SHU
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong (email: [email protected]) School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: [email protected])
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Abstract

We investigate the relationship between Poincaré recurrence and topological entropy of a dynamical system (X,f). For , let D(α,β) be the set of x with lower and upper recurrence rates α and β, 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 , has the full topological entropy of X. This extends a result of Feng and Wu [The Hausdorff dimension of recurrence sets in symbolic spaces. Nonlinearity14 (2001), 81–85] for symbolic spaces.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 6 , December 2008 , pp. 1917 - 1943
Copyright
Copyright © 2008 Cambridge University Press

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