Advances on Stable Ergodicity of Toral Automorphisms
Dynamical Systems
2026-03-26 v1
Abstract
We prove that all ergodic automorphisms of the -dimensional torus with two dimensional center are stably ergodic. This includes all ergodic automorphisms in dimension or . 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.
Cite
@article{arxiv.2603.23778,
title = {Advances on Stable Ergodicity of Toral Automorphisms},
author = {Fernando Argentieri and Andrea Ulliana},
journal= {arXiv preprint arXiv:2603.23778},
year = {2026}
}