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PreprintCC BY 4.0arXiv

Unstable entropy for Anosov diffeomorphisms on tori isotopic to Anosov linear maps

  • Tristan Humbert
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Abstract

Let f be an Anosov diffeomorphism on the d-torus which is strongly partially hyperbolic with expanding center. If d=3 or if f is isotopic to its linear part, where the isotopy is contained in the set of partially hyperbolic diffeomorphisms, we construct systems of strong-unstable and center-stable Margulis measures which are holonomy invariant. As a consequence, we obtain a characterization of measures of maximal unstable entropy in terms of their conditional measures along strong-unstable leaves. Moreover, we show that the unstable topological entropy, a measure of maximal unstable entropy and the Margulis system can be retrieved from the Pollicott-Ruelle spectrum of f.

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Cite

BibTeXRIS
BibTeX
@misc{humbert2026unstable,
  title = {{Unstable entropy for Anosov diffeomorphisms on tori isotopic to Anosov linear maps}},
  author = {Tristan Humbert},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24647},
  eprint = {2610.24647},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24647},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Unstable entropy for Anosov diffeomorphisms on tori isotopic to Anosov linear maps
AU  - Tristan Humbert
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24647
UR  - https://arxiv.org/abs/2610.24647
AB  - Let f be an Anosov diffeomorphism on the d-torus which is strongly partially hyperbolic with expanding center. If d=3 or if f is isotopic to its linear part, where the isotopy is contained in the set of partially hyperbolic diffeomorphisms, we construct systems of strong-unstable and center-stable Margulis measures which are holonomy invariant. As a consequence, we obtain a characterization of measures of maximal unstable entropy in terms of their conditional measures along strong-unstable leaves. Moreover, we show that the unstable topological entropy, a measure of maximal unstable entropy and the Margulis system can be retrieved from the Pollicott-Ruelle spectrum of f.
ER  -