Topological attractors of quasi-periodically forced one-dimensional maps [ Back ]

Date:
21.01.19   
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Zhaoyang Dong
University:
Universitat Autònoma de Barcelona
Abstract

We investigate the topological attractors of some quasi-periodically forced one-dimensional maps, which are in form of\[F(\theta,x) = (\, \theta + \omega \mbox{\ mod(1)}, \, \psi(\theta,x) \,),\]where $(\theta, x) \in \mathbb{S}^1 \times \mathbb{R} $, $\omega$ is a fixed irrational real number and the function $\psi(\theta,x)$ is continuous on both $x$ and $\theta$. We present some simple but essential properties of the topological structure of their attractors, and elaborate the dynamics of two types of specific systems. The first type consists of two quasi-periodically forced increasing real maps, whose dynamics displays clearly the basic distinction between the pinched and non-pinched cases. The other type is forced S-unimodal maps. We propose the mechanism for the change of periodicity of their attractors according to the forced terms. This is based on our analysis of the block structure of topological attractors of unforced S-unimodal maps, and is substantiated by numerical evidence.