# zbMATH — the first resource for mathematics

Heteroclinic cycles and homoclinic closures for generic diffeomorphisms. (English) Zbl 1034.37013
Summary: We prove some $$C^1$$ generic results about orbit-connecting, in particular about heteroclinic cycles and homoclinic closures. As a consequence we obtain a three-ways $$C^1$$ density theorem: Diffeomorphisms with either infinitely many weakly transitive components or a heterodimensional cycle are $$C^1$$ dense in the complement of the $$C^1$$ closure of Axiom A and no-cycle diffeomorphisms.

##### MSC:
 37C29 Homoclinic and heteroclinic orbits for dynamical systems 37C05 Dynamical systems involving smooth mappings and diffeomorphisms 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Full Text: