English

Totally ergodic generalised matrix equilibrium states have the Bernoulli property

Dynamical Systems 2022-10-19 v1

Abstract

We show that every totally ergodic generalised matrix equilibrium state is psi-mixing with respect to the natural partition into cylinders and hence is measurably isomorphic to a Bernoulli shift in its natural extension. This implies that the natural extensions of ergodic generalised matrix equilibrium states are measurably isomorphic to Bernoulli processes extended by finite rotations. This resolves a question of Gatzouras and Peres in the special case of self-affine repelling sets with generic translations.

Keywords

Cite

@article{arxiv.2011.11497,
  title  = {Totally ergodic generalised matrix equilibrium states have the Bernoulli property},
  author = {Ian D. Morris},
  journal= {arXiv preprint arXiv:2011.11497},
  year   = {2022}
}