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ATTRACTORS OF GENERIC DIFFEOMORPHISMS ARE AVIO ABDENUR
 

Summary: ATTRACTORS OF GENERIC DIFFEOMORPHISMS ARE
PERSISTENT
FL 
AVIO ABDENUR
Abstract. We prove that given a compact n-dimensional 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 di eomorphisms
always admit weakly hyperbolic dominated splittings; in particular, given
any surface di eomorphism f in a residual subset of Di 1 (M 2 ), then
every

17147 - transitive set of f (such as a transitive attractor) is

  

Source: Abdenur, Flavio - Departamento de Matemática, Pontifícia Universidade Católica do Rio Grande do Sul

 

Collections: Mathematics