English

Advances on Stable Ergodicity of Toral Automorphisms

Dynamical Systems 2026-03-26 v1

Abstract

We prove that all ergodic automorphisms of the NN-dimensional torus with two dimensional center are stably ergodic. This includes all ergodic automorphisms in dimension N5N\leq 5 or N=7N=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.

Keywords

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}
}