Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three
Dynamical Systems
2025-06-03 v1
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.
Keywords
Cite
@article{arxiv.2506.00405,
title = {Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three},
author = {Ziqiang Feng and Raúl Ures},
journal= {arXiv preprint arXiv:2506.00405},
year = {2025}
}
Comments
41 pages. This is a preliminary version