Dynamics of two dimensional Blaschke products.
Mike Shub | Pujals, Enrique R.
In this paper we study the dynamics on $\TT^2$ and $\CC^2$ of a two dimensional Blaschke product. We prove that in the case that the Blaschke product is a diffeomorphisms of $\TT^2$ with all periodic points hyperbolic then the dynamics is hyperbolic. If a two dimensional Blaschke product diffeomorphism of $\TT^2$ is embedded in a two dimensional family given by composition with translations of $\TT^2,$ then we show that there is an open set of parameter values for which the dynamics is Anosov or has an expanding attractor with a unique SRB measure.