Abstract:

We consider maps $F(theta,z)=(theta+omega,a(theta)z)$ where $theta$ belongs to the one-dimensional torus, $z$ is complex and $a(theta)$ is a smooth map such that $a(theta)$ is also a complex number for all $theta$. We call these maps linear skew products. The goal of this talk is to classify via conjugacy these kind of maps when $omega$ is a diophantine number. In particular, we can determine when a linear skew product is reducible and obtain simple results for two-dimensional real skew products.