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Morse-Smale systems and horseshoes for three dimensional singular flows

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arxiv 1302.0946 v1 pith:U4KYBDIE submitted 2013-02-05 math.DS

Shaobo Gan , Dawei Yang This is my paper · ORCID
classification math.DS
keywords accumulatedmorse-smaleonesdimensionaleithereveryfieldflows
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abstract

We prove that for every three-dimensional vector field, either it can be accumulated by Morse-Smale ones, or it can be accumulated by ones with a transverse homoclinic intersection of some hyperbolic periodic orbit in the $C^1$ topology.

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  1. Finiteness of homoclinic classes on sectional hyperbolic sets

    math.DS 2019-08 reject novelty 5.0 of 10

    For any C1 perturbation of a vector field with a sectional hyperbolic set, the number of homoclinic classes inside a fixed neighborhood is uniformly bounded.

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