Recurrence times and rates of mixing.

*(English)*Zbl 0983.37005Summary: 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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