TY - JOUR
T1 - Robust transitivity and topological mixing for C1-flows
AU - Abdenur, Flavio
AU - Avila, Artur
AU - Bochi, Jairo
PY - 2004/3
Y1 - 2004/3
N2 - We prove that nontrivial homoclinic classes of Cr-generic flows are topologically mixing. This implies that given Λ, a nontrivial C 1-robustly transitive set of a vector field X, there is a C 1 -perturbation Y of X such that the continuation Λ Y of Λ is a topologically mixing set for Y. In particular, robustly transitive flows become topologically mixing after C 1-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 nontrivial homoclinic classes are topologically mixing is not open and dense, in general.
AB - We prove that nontrivial homoclinic classes of Cr-generic flows are topologically mixing. This implies that given Λ, a nontrivial C 1-robustly transitive set of a vector field X, there is a C 1 -perturbation Y of X such that the continuation Λ Y of Λ is a topologically mixing set for Y. In particular, robustly transitive flows become topologically mixing after C 1-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 nontrivial homoclinic classes are topologically mixing is not open and dense, in general.
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U2 - 10.1090/s0002-9939-03-07187-9
DO - 10.1090/s0002-9939-03-07187-9
M3 - Article
AN - SCOPUS:1442302799
VL - 132
SP - 699
EP - 705
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 3
ER -