Generic Robustness of Spectral Decompositions

Flavio Abdenur

Keywords: Generic properties | spectral decomposition

We prove that, C1-generically in Diff1(M), spectral decompositions (ie, partitions of the nonwandering set into finite number of pairwise disjoint transitive sets) are robust in a generic sense. This implies that generic diffeomorphisms with spectral decompositions are Axiom A if and onlu if they are ``far from'' heterodimensional cycles, a type of homoclinic bifurcation.

Anexos:

• new3.dvi