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PreprintarXiv licencearXiv

Expanding on Average Diffeomorphisms

  • Pablo D. Carrasco
  • Davi Obata
  • Radu Saghin
  • Jiagang Yang
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Abstract

We study the statistical properties of partially hyperbolic diffeomorphisms with a two-dimensional center exhibiting mixed behavior, without assuming a dominated splitting inside the center. We introduce the notion of an expanding on average for partially hyperbolic diffeomorphism and, under a center jacobian assumption, we prove the existence of finitely many ergodic hyperbolic SRB measures, and show the strong positive recurrence property, which implies that each SRB measure, up to a period, satisfies exponential decay of correlations, among other strong statistical laws. We apply our results to several examples.

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Cite

BibTeXRIS
BibTeX
@misc{carrasco2026expanding,
  title = {{Expanding on Average Diffeomorphisms}},
  author = {Pablo D. Carrasco and Davi Obata and Radu Saghin and Jiagang Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25559},
  eprint = {2610.25559},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25559},
}
RIS
TY  - UNPB
TI  - Expanding on Average Diffeomorphisms
AU  - Pablo D. Carrasco
AU  - Davi Obata
AU  - Radu Saghin
AU  - Jiagang Yang
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25559
UR  - https://arxiv.org/abs/2610.25559
AB  - We study the statistical properties of partially hyperbolic diffeomorphisms with a two-dimensional center exhibiting mixed behavior, without assuming a dominated splitting inside the center. We introduce the notion of an expanding on average for partially hyperbolic diffeomorphism and, under a center jacobian assumption, we prove the existence of finitely many ergodic hyperbolic SRB measures, and show the strong positive recurrence property, which implies that each SRB measure, up to a period, satisfies exponential decay of correlations, among other strong statistical laws. We apply our results to several examples.
ER  -