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arXiv · 2506.00405

Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

Ziqiang Feng·Raúl Ures
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Abstract

We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic, giving an affirmative answer to the Hertz-Hertz-Ures Ergodicity Conjecture in the homotopy class of identity.

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Ziqiang Feng, Raúl Ures. 2025-05-31. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three. https://arxiv.org/abs/2506.00405

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