A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

Volume 238 / 2017

Alexey Korepanov, Zemer Kosloff, Ian Melbourne Studia Mathematica 238 (2017), 59-89 MSC: Primary 34C29; Secondary 37D25, 34E13. DOI: 10.4064/sm8540-1-2017 Published online: 12 April 2017

Abstract

We consider families of fast-slow skew product maps of the form $$ x_{n+1} = x_n+{\epsilon }a(x_n,y_n,{\epsilon }),\ \hskip 1em y_{n+1} = T_{\epsilon }y_n, $$ where $T_{\epsilon }$ is a family of nonuniformly expanding maps, and prove averaging and rates of averaging for the slow variables $x$ as ${\epsilon }\to 0$. Similar results are obtained also for continuous time systems $$ \dot x = {\epsilon }a(x,y,{\epsilon }),\ \hskip 1em \dot y = g_{\epsilon }(y). $$

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.

Authors

  • Alexey KorepanovMathematics Institute
    University of Warwick
    Coventry, CV4 7AL, UK
    e-mail
  • Zemer KosloffMathematics Institute
    University of Warwick
    Coventry, CV4 7AL, UK
    and
    Permanent address:
    Einstein Institute of Mathematics
    The Hebrew University
    Edmond J. Safra Campus (Givat Ram)
    Jerusalem 91904, Israel
    e-mail
  • Ian MelbourneMathematics Institute
    University of Warwick
    Coventry, CV4 7AL, UK
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image