## Abstract

We consider dynamical systems (X, T, μ) which have exponential decay of correlations for either Hölder continuous functions or functions of bounded variation. Given a sequence of balls (Bn)n=1∞, we give sufficient conditions for the set of eventually always hitting points to be of full measure. This is the set of points x such that for all large enough m, there is a k< m with T^{k}(x) ∈ B_{m}. We also give an asymptotic estimate as m→ ∞ on the number of k< m with T^{k}(x) ∈ B_{m}. As an application, we prove for almost every point x an asymptotic estimate on the number of k≤ m such that a_{k}≥ m^{t}, where t∈ (0 , 1) and a_{k} are the continued fraction coefficients of x.

Original language | English |
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Pages (from-to) | 763-784 |

Journal | Monatshefte fur Mathematik |

Volume | 196 |

Issue number | 4 |

Early online date | 2021 Aug 28 |

DOIs | |

Publication status | Published - 2021 |

## Subject classification (UKÄ)

- Mathematical Analysis

## Free keywords

- Continued fractions
- Eventually always hitting points
- Shrinking targets