Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
ROBUST TRANSITIVITY AND TOPOLOGICAL MIXING FOR FLAVIO ABDENUR, ARTUR AVILA AND JAIRO BOCHI
 

Summary: ROBUST TRANSITIVITY AND TOPOLOGICAL MIXING FOR
C1
-FLOWS
FLAVIO ABDENUR, ARTUR AVILA AND JAIRO BOCHI
Abstract. We prove that non-trivial homoclinic classes of Cr-generic flows are topo-
logically mixing. This implies that given a non-trivial C1-robustly transitive set of
a vector field X, there is a C1-perturbation Y of X such that the continuation Y of
is a topologically mixing set for Y . In particular, robustly transitive flows become
topologically mixing after C1-perturbations. These results generalize a theorem by
Bowen on the basic sets of generic Axiom A flows. We also show that the set of flows
whose non-trivial homoclinic classes are topologically mixing is not open and dense,
in general.
2000 Mathematics Subject Classification: 37C20.
Key words: generic properties of flows, homoclinic classes, topological mixing.
1. Statement of the Results
Throughout this paper M denotes a compact d-dimensional boundaryless manifold,
d 3, and Xr
(M) is the space of Cr
vector fields on M endowed with the usual Cr
topology, where r 1 . We shall prove that, generically (residually) in Xr

  

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

 

Collections: Mathematics