Abstract

We work with two-dimensional skew-products defined on the cylinder $(mathbb{S}^1timesmathbb{R})$ of the form [ begin{cases} theta_{n+1}=R(theta_n),\ x_{n+1}=f(x_n)g(theta_n)end{cases} ] where (R) is a continuous degree-one circle map, and (f) satisfies some properties of concavity and monotonicity. We prove that when (R) has no periodic points, there exists finitely many attracting sets. In contrast when the rotation interval of any of the lifts of (R) is non-degenerate, we prove the existence of uncountably many attracting sets, each of them related with an irrational rotation number.

This is a joined work with Lluís Alsedà (UAB).