Boris Petkovi'c

Topological centralizers of perturbations of ergodic toral automorphisms with two dimensional center

Let $A$ be an ergodic linear automorphism of the torus $\T^N$ whose center space has dimension two. We prove a dichotomy result that for every $f \in \mathcal{U}$, where $\mathcal{U}$ is the $C^{22}$ neighborhood of $A$ inside volume preserving diffeomorphisms on $\T^N$, exactly one of two alternatives holds. Either $f...