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arXiv · 1509.06772

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

A. Korepanov·Z. Kosloff·I. Melbourne
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Abstract

We consider families of fast-slow skew product maps of the form \begin{align*} x_{n+1} = x_n+εa(x_n,y_n,ε), \quad y_{n+1} = T_εy_n, \end{align*} where $T_ε$ is a family of nonuniformly expanding maps, and prove averaging and rates of averaging for the slow variables $x$ as $ε\to0$. Similar results are obtained also for continuous time systems \begin{align*} \dot x = εa(x,y,ε), \quad \dot y = g_ε(y). \end{align*} 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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A. Korepanov, Z. Kosloff, I. Melbourne. 2016-02-11. Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems. https://arxiv.org/abs/1509.06772

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