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PreprintarXiv licencearXiv

Pesin's entropy formula on attractors with continuous invariant splittings

  • Xinyu Bai
  • Wanshan Lin
  • Xueting Tian
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Abstract

Under quantitative asymptotic hyperbolicity assumptions, we prove the existence of hyperbolic ergodic invariant probability measures satisfying Pesin's entropy formula for C1 diffeomorphisms whose attractors admit extendable continuous invariant splittings. No dominated splitting is required on the attractor. For C1+α diffeomorphisms, the resulting measures are SRB measures. Our results apply to mostly expanding partially hyperbolic systems and to systems with strictly separated Lyapunov exponents under suitable statistical assumptions. We also construct examples with hyperbolic SRB measures of full support on attractors admitting no nontrivial dominated splitting, demonstrating the applicability of our criteria beyond results that require domination.

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Cite

BibTeXRIS
BibTeX
@misc{bai2026pesins,
  title = {{Pesin's entropy formula on attractors with continuous invariant splittings}},
  author = {Xinyu Bai and Wanshan Lin and Xueting Tian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32820},
  eprint = {2610.32820},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32820},
}
RIS
TY  - UNPB
TI  - Pesin's entropy formula on attractors with continuous invariant splittings
AU  - Xinyu Bai
AU  - Wanshan Lin
AU  - Xueting Tian
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.32820
UR  - https://arxiv.org/abs/2610.32820
AB  - Under quantitative asymptotic hyperbolicity assumptions, we prove the existence of hyperbolic ergodic invariant probability measures satisfying Pesin's entropy formula for C^1 diffeomorphisms whose attractors admit extendable continuous invariant splittings. No dominated splitting is required on the attractor. For C^1+α diffeomorphisms, the resulting measures are SRB measures. Our results apply to mostly expanding partially hyperbolic systems and to systems with strictly separated Lyapunov exponents under suitable statistical assumptions. We also construct examples with hyperbolic SRB measures of full support on attractors admitting no nontrivial dominated splitting, demonstrating the applicability of our criteria beyond results that require domination.
ER  -