Unstable entropy for Anosov diffeomorphisms on the 3-torus
Abstract
For Anosov diffeomorphisms on the -torus which are strongly partially hyperbolic with expanding center, we construct systems of strong unstable and center stable Margulis measures which are holonomy-invariant. This allows us to obtain a characterization of the measures of maximal unstable entropy in terms of their conditional measures along the strong unstable leaves. Moreover, we show that the Margulis systems identify with Pollicott-Ruelle (co)-resonant states for the action on 2-forms. This shows that the unstable topological entropy and a measure of maximal unstable entropy can be retrieved from the spectral approach.
Keywords
Cite
@article{arxiv.2509.09520,
title = {Unstable entropy for Anosov diffeomorphisms on the 3-torus},
author = {Tristan Humbert},
journal= {arXiv preprint arXiv:2509.09520},
year = {2025}
}
Comments
The argument given in Remark 3 was incomplete, this issue has now been resolved. A small gap in the previous proof of Proposition 3.4 was also fixed. A new remark (Remark 2) was added