Korepanov, Alexey, Kosloff, Zemer and Melbourne, Ian (2017) Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems. Studia Mathematica, 238 . pp. 59-89. doi:10.4064/sm8540-1-2017 ISSN 0039-3223.

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Abstract

We consider families of fast-slow skew product maps of the form

xn+1=xn+ϵa(xn,yn,ϵ), yn+1=Tϵyn,

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

x˙=ϵa(x,y,ϵ), y˙=gϵ(y).

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Averaging method (Differential equations)
Journal or Publication Title:	Studia Mathematica
Publisher:	Polska Akademia Nauk
ISSN:	0039-3223
Official Date:	12 April 2017
Dates:	Date Event 12 April 2017 Published 16 January 2017 Accepted
Volume:	238
Page Range:	pp. 59-89
DOI:	10.4064/sm8540-1-2017
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	31 January 2017
Date of first compliant Open Access:	28 September 2017
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID AdG 320977 European Research Council http://dx.doi.org/10.13039/501100000781
Related URLs:	Publisher

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