Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

2025/05/31 by Feng, Ziqiang, Ures, Raúl
#37A25 #37C86 #37D30 #57R30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.00405

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.

Related

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