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New examples of stably ergodic diffeomorphisms in dimension 3

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arxiv 2004.10844 v2 pith:QYXNZ4MH submitted 2020-04-22 math.DS

Gabriel Nuñez , Davi Obata , Jana Rodriguez Hertz This is my paper · ORCID
classification math.DS
keywords ergodicstablydiffeomorphismdiffeomorphismsdimensionalexampleshyperbolicvolume
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abstract

We prove that in the isotopy class of any volume preserving partially hyperbolic diffeomorphism in a $3$-dimensional manifold, there is a non-partially hyperbolic stably ergodic diffeomorphism. In particular, we provide new examples of stably ergodic diffeomorphisms in 3-dimensional manifolds with respect to a smooth volume measure.

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  1. Stable minimality of expanding foliations

    math.DS 2019-08 conditional novelty 7.0 of 10

    For generic volume-preserving diffeomorphisms, a minimal expanding foliation with a matching-index periodic point is stably minimal, yielding robust mixing and an essentially dense hyperbolic ergodic component.

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