Conservative partially hyperbolic diffeomorphisms isotopic to the identity on Seifert 3-manifolds are ergodic.
$C^1$ density of stable ergodicity
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abstract
We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense. To establish these results, we develop new perturbation tools for the $C^1$ topology: linearization of horseshoes while preserving entropy, and creation of "superblenders" from hyperbolic sets with large entropy.
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math.DS 1years
2019 1verdicts
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Ergodicity and partial hyperbolicity on Seifert manifolds
Conservative partially hyperbolic diffeomorphisms isotopic to the identity on Seifert 3-manifolds are ergodic.