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Recurrence, dimensions, and Lyapunov exponents. (English) Zbl 1138.37300
Summary: We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.

MSC:
37A05 Dynamical aspects of measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
37C45 Dimension theory of smooth dynamical systems
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37E05 Dynamical systems involving maps of the interval
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