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

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 $T_{\epsilon }$ 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 \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.

Shortened version. First order averaging moved into a remark. Explicit coupling argument moved into a separate note

References in corpus (3)

• On the susceptibility function of piecewise expanding interval maps
• Linear response for intermittent maps
• Statistical stability of equilibrium states for interval maps

Cited by in corpus (1)

• Statistical properties for flows with unbounded roof function, including the Lorenz attractor