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Most Invariant Manifolds of Conservative Systems have Transitive Closure

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Abstract

The main result of this work in the following: for generic volume preserving flows on compact manifolds with the \(C^r\) topology, \(1\le r\le \infty \), the closure of every invariant manifold of periodic orbits and singularities is a chain transitive set. This was already known for generic symplectic and volume preserving diffeomorphisms.

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Authors and Affiliations

  1. Departamento de Matemática Centro de Ciências Exatas, Universidade Federal do Espírito Santo, Vitória, Brazil

    Fábio Castro

  2. Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Fernando Oliveira

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  1. Fábio Castro
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  2. Fernando Oliveira
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Correspondence to Fábio Castro.

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Castro, F., Oliveira, F. Most Invariant Manifolds of Conservative Systems have Transitive Closure. Differ Equ Dyn Syst 32, 1–13 (2024). https://doi.org/10.1007/s12591-020-00554-4

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  • DOI: https://doi.org/10.1007/s12591-020-00554-4

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