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

Abstract

In this paper we study flows having an isolated non-saddle set. We see that the global structure of a flow having an isolated non-saddle set K depends on the way K sits in the phase space at the cohomological level. We construct flows on surfaces having isolated non-saddle sets with a prescribed global structure. We also study smooth parametrized families of flows and continuations of isolated non-saddle sets.