Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems

Alexey Korepanov; Zemer Kosloff; Ian Melbourne

doi:10.4064/sm8540-1-2017

Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems

Alexey Korepanov, Zemer Kosloff, Ian Melbourne

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We consider families of fast-slow skew product maps of the form {equation presented} where T_ϵ is a family of nonuniformly expanding maps, and prove averaging and rates of averaging for the slow variables x as ϵ → 0. Similar results are obtained also for continuous time systems {equation presented} Our results include cases where the family of fast dynamical systems consists of intermittent maps, unimodal maps (along the Collet{Eckmann parameters) and Viana maps.

Original language	English
Pages (from-to)	59-89
Number of pages	31
Journal	Studia Mathematica
Volume	238
Issue number	1
DOIs	https://doi.org/10.4064/sm8540-1-2017
State	Published - 2017

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2017.

Keywords

Averaging
Deterministic
Dimension reduction
Fast-slow
Nonuniformly hyperbolic

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10.4064/sm8540-1-2017

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abstract = "We consider families of fast-slow skew product maps of the form {equation presented} where Tϵ is a family of nonuniformly expanding maps, and prove averaging and rates of averaging for the slow variables x as ϵ → 0. Similar results are obtained also for continuous time systems {equation presented} Our results include cases where the family of fast dynamical systems consists of intermittent maps, unimodal maps (along the Collet{Eckmann parameters) and Viana maps.",

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PY - 2017

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KW - Deterministic

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Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems

Abstract

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Keywords

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