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arXiv · 2001.06502

Cech cohomology, homoclinic trajectories and robustness of non-saddle sets

Héctor Barge
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Abstract

In this paper we study flows $\varphi:M\times\mathbb{R}\longrightarrow M$ having an isolated non-saddle set. We see that the complexity of the region of influence of an isolated non-saddle set $K$ depends on the way in which $K$ sits on the phase space at the cohomological level. We construct flows in surfaces having isolated non-saddle sets with a prescribed structure for its region of influence. We also study parametrized families of smooth flows and continuations of non-saddle sets.

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Héctor Barge. 2020-01-17. Cech cohomology, homoclinic trajectories and robustness of non-saddle sets. https://doi.org/10.3934/dcds.2020381

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