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arXiv · 2610.32820

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 $C^1$ 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.

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Xinyu Bai, Wanshan Lin, Xueting Tian. 2026-10-23. Pesin's entropy formula on attractors with continuous invariant splittings. https://arxiv.org/abs/2610.32820

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