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.",

keywords = "Averaging, Deterministic, Dimension reduction, Fast-slow, Nonuniformly hyperbolic",

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AU - Kosloff, Zemer

AU - Melbourne, Ian

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2017.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Averaging

KW - Deterministic

KW - Dimension reduction

KW - Fast-slow

KW - Nonuniformly hyperbolic

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JO - Studia Mathematica

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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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