On the Transitivity of Invariant Manifolds of Conservative Flows

Fábio Castro; Fernando Oliveira

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arXiv · 1503.00182

On the Transitivity of Invariant Manifolds of Conservative Flows

Fábio Castro·Fernando Oliveira

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Abstract

The main result of this work is the following: for volume preserving flows on compact manifolds with the $C^r$ topology, $1 \leqq r \leqq \infty$ , the closure of every invariant manifold of periodic orbits and singularities is a chain transitive set. We also develop to new local constructions, which surprise by the simplicity of the arguments. One, a local perturbation to change an orbit to a nearby without altering its past. The other is a flow box theorem in the context of volume preserving flows, a result that is well known for Hamiltonians or general flows.

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Fábio Castro, Fernando Oliveira. 2015-02-28. On the Transitivity of Invariant Manifolds of Conservative Flows. https://arxiv.org/abs/1503.00182

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