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arXiv · 2011.11497

Totally ergodic generalised matrix equilibrium states have the Bernoulli property

Ian D. Morris
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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.

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Ian D. Morris. 2020-11-23. Totally ergodic generalised matrix equilibrium states have the Bernoulli property. https://doi.org/10.1007/s00220-021-04200-0

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