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Recurrence times and rates of mixing. (English) Zbl 0983.37005
Summary: The setting of this paper consists of a map making “nice” returns to a reference set. Criteria for the existence of equilibria, speed of convergence to equilibria and for the central limit theorem are given in terms of the tail of the return time function. The abstract setting considered arises naturally in differentiable dynamical systems with some expanding or hyperbolic properties.

MSC:
37A25 Ergodicity, mixing, rates of mixing
37B20 Notions of recurrence and recurrent behavior in topological dynamical systems
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
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