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

Abstract

In this paper we study flows $\phi :M\times \mathbb{R}⟶M$ 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.

arXiv comment22 pages, 8 figures

References in corpus (2)

• Regular blocks and Conley index of isolated invariant continua in surfaces
• Dissonant points and the region of influence of non-saddle sets

Cited by in corpus (1)

• Shape index, Brouwer degree and Poincaré-Hopf theorem