Transitive partially hyperbolic diffeomorphisms in dimension three
Abstract
We prove that any C1+α transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of FP-classify, this establishes the equivalence between transitivity and ergodicity for C1+α conservative partially hyperbolic diffeomorphisms in any closed 3-manifold. Moreover, we provide a characterization of compact accessibility classes under transitivity, thereby giving a precise classification of all accessibility classes for transitive 3-dimensional partially hyperbolic diffeomorphisms.
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