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arXiv · 2603.23778

Advances on Stable Ergodicity of Toral Automorphisms

Fernando Argentieri·Andrea Ulliana
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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 $N\leq 5$ 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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Fernando Argentieri, Andrea Ulliana. 2026-03-24. Advances on Stable Ergodicity of Toral Automorphisms. https://arxiv.org/abs/2603.23778

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