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Loss of Memory and Moment Bounds for Nonstationary Intermittent Dynamical Systems

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Abstract

We study nonstationary intermittent dynamical systems, such as compositions of a (deterministic) sequence of Pomeau–Manneville maps. We prove two main results: sharp bounds on memory loss, including the “unexpected” faster rate for a large class of measures, and sharp moment bounds for Birkhoff sums and, more generally, “separately Hölder” observables.

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Notes

  1. Most spaces are universally measurable, see Shortt [37].

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Acknowledgements

A.K. is supported by an Engineering and Physical Sciences Research Council grant EP/P034489/1. J.L. received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 787304). The authors thank Viviane Baladi, Mark Holland and universities of Exeter and Sorbonne for support and hospitality during their visits.

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Authors and Affiliations

  1. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QF, UK

    A. Korepanov

  2. Laboratoire de Probabilités, Statistique et Modélisation (LPSM), CNRS, Sorbonne Université, Université de Paris, 4 Place Jussieu, 75005, Paris, France

    J. Leppänen

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  1. A. Korepanov
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  2. J. Leppänen
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Correspondence to A. Korepanov.

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Communicated by C. Liverani.

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Korepanov, A., Leppänen, J. Loss of Memory and Moment Bounds for Nonstationary Intermittent Dynamical Systems. Commun. Math. Phys. 385, 905–935 (2021). https://doi.org/10.1007/s00220-021-04071-5

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  • DOI: https://doi.org/10.1007/s00220-021-04071-5

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