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2020•arXiv (Cornell University)Open access

New examples of stably ergodic diffeomorphisms in dimension 3

Nu\~nez, Gabriel, Davi Obata, Jana Rodriguez Hertz

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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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What this paper is about

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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Available 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.

Key concepts: Diffeomorphism, Ergodic theory, Isotopy, Mathematics, Pure mathematics, Manifold (fluid mechanics), Dimension (graph theory), Measure (data warehouse)

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