Preprint A99/2001
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.