ROBUST HETERODIMENSIONAL CYCLES AND $C^1$-GENERIC DYNAMICS

Abstract

A diffeomorphism -generic dynamics (in any dimension). Two of such consequences are the following. For tame diffeomorphisms (generic diffeomorphisms with finitely many chain recurrence classes) there is the following dichotomy: either the system is hyperbolic or it has a robust heterodimensional cycle. Moreover, any chain recurrence class containing saddles having different indices has a robust cycle.