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Pesin’s dimension for Poincaré recurrences. (English) Zbl 0933.37019
Summary: A new characteristic of Poincaré recurrences is introduced. It describes an average return time in the framework of a general construction for dimension-like characteristics. Some examples are considered including rotations on the circle and the Denjoy example.

MSC:
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37B20 Notions of recurrence and recurrent behavior in topological dynamical systems
37E05 Dynamical systems involving maps of the interval
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References:
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[2] DOI: 10.1063/1.166252 · Zbl 0933.37024
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