## A fractalization process for affine skew-products on the complex plane

Series:
CDSNS Colloquium
Wednesday, May 10, 2017 - 13:00
1 hour (actually 50 minutes)
Location:
Skiles 005
,
Universitat de Barcelona
Organizer:
Consider an affine skew product of the complex plane. $$\begin{cases} \omega \mapsto \theta+\omega,\\ z \mapsto =a(\theta \mu)z+c, \end{cases}$$where $\theta \in \mathbb{T}$, $z\in \mathbb{C}$, $\omega$ is Diophantine, and $\mu$ and $c$ are real parameters. In this talk we show that, under suitable conditions, the affine skew product has an invariant curve that undergoes a fractalization process when $\mu$ goes to a critical value. The main hypothesis needed is the lack of reducibility of the system.  A characterization of reducibility of linear skew-products on the complex plane is provided. We also include a linear and topological classification of these systems. Join work with: N\'uria Fagella, \`Angel Jorba and Joan Carles Tatjer