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arXiv · 2610.25559

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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Pablo D. Carrasco, Davi Obata, Radu Saghin, Jiagang Yang. 2026-10-18. Expanding on Average Diffeomorphisms. https://arxiv.org/abs/2610.25559

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