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

作者：Korepanov Alexey^*; Melbourne Ian; Kosloff Zemer

来源：Studia Mathematica, 2017, 238(1): 59-89.

DOI：10.4064/sm8540-1-2017

• averaging
• deterministic
• fast-slow
• nonuniformly hyperbolic
• dimension reduction

We consider families of fast-slow skew product maps of the form
x(n+1) = x(n) + epsilon a(x(n),y(n),epsilon), y(n+1) = T-epsilon yn
where T-epsilon is a family of nonuniformly expanding maps, and prove averaging and rates of averaging for the slow variables x as epsilon -> 0. Similar results are obtained also for continuous time systems
x = epsilon a(x,y,epsilon), y = g(epsilon)(y).
Our results include cases where the family of fast dynamical systems consists of intermittent maps, unimodal maps (along theCollet-Eckmann parameters) and Viana maps.

• 出版日期2017