### Abstract

A dynamical array consists of a family of functions {f_{n,i}1 : 1 ≤ i ≤ k_{n}, n ≥ 1} and a family of initial times {τ_{n,i} : 1 ≤ i ≤ k_{n}, n ≥ 1}. For a dynamical system (X, T) we identify distributional limits for sums of the form S_{n} = 1/s_{n} ^{kn}_{i=1} [f_{n,i} T^{Tn,i} - a_{n,i}] n ≥ 1 for suitable (non-random) constants s_{n} > 0 and a_{n,i} ϵ ℝ. We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from GibbsMarkov systems. Our results, which hold for more general dynamics, are stated in the context of GibbsMarkov dynamical systems for convenience.

Original language | English (US) |
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Pages (from-to) | 4587-4613 |

Number of pages | 27 |

Journal | Nonlinearity |

Volume | 30 |

Issue number | 12 |

DOIs | |

State | Published - Nov 16 2017 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

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## Cite this

*Nonlinearity*,

*30*(12), 4587-4613. https://doi.org/10.1088/1361-6544/aa8ca2