 
Summary: ATTRACTORS OF GENERIC DIFFEOMORPHISMS ARE
PERSISTENT
FL
AVIO ABDENUR
Abstract. We prove that given a compact ndimensional boundaryless
manifold M , n 2, there exists a residual subset R of Di 1 (M) such
that if is
an
21202 4 and transitive set of f 2 R, then admits a
continuation in a generic neighborhood of f ; such sets are called almost
robustly transitive or generically transitive sets. Furthermore, if is a
transitive attractor of f , then the continuation of is also an attractor.
This implies
that
t 23470 transitive sets of generic dieomorphisms
always admit weakly hyperbolic dominated splittings; in particular, given
any surface dieomorphism f in a residual subset of Di 1 (M 2 ), then
every
17147  transitive set of f (such as a transitive attractor) is
