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arXiv · 2607.04496

Robust transitivity versus trapping regions for partially hyperbolic diffeomorphisms

Sylvain Crovisier·Rafael Potrie
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Abstract

We show that among partially hyperbolic diffeomorphisms with one dimensional center there is a $C^1$-open and dense subset for which either there is a proper quasi-attractor or both strong foliations are minimal. The same result holds among volume-preserving partially hyperbolic diffeomorphisms and has consequences about robust transitivity beyond the conservative setting. The proofs involve a careful study of minimal $\mathcal{W}^u$-saturated sets and interact with recent results in the subject.

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Sylvain Crovisier, Rafael Potrie. 2026-07-05. Robust transitivity versus trapping regions for partially hyperbolic diffeomorphisms. https://arxiv.org/abs/2607.04496

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