Abstract:The coexistence of singularities and regular orbits in chain transitive sets has been a major obstacle in understanding the hyperbolic/partial hyperbolic nature of robust dynamics. Notably, the vector fields with all periodic orbits robustly hyperbolic (star flows), are hyperbolic in absence of singularities.Morales, Pacifico and Pujals proposed a partial hyperbolicity called "singular hyperbolicity" that characterizes an open and dense subset of three dimensional star flows. In higher dimensions, Bonatti and … Show more
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