Advances on Stable Ergodicity of Toral Automorphisms
Abstract
We prove that all ergodic automorphisms of the N-dimensional torus with two dimensional center are stably ergodic. This includes all ergodic automorphisms in dimension N≤ 5 or N=7. This generalizes a previous result of Rodriguez-Hertz, that required an additional algebraic condition on the carachteristic polynomial of the linear automorphism. The core of the proof is a minimality criterion.
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