Mixing attractors for 3-flows

被引:26
作者
Morales, CA [1 ]
Pacifico, MJ [1 ]
机构
[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil
关键词
D O I
10.1088/0951-7715/14/2/310
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove that every non-trivial attractor is mixing for a generic 3-flow in G(1)(M), the interior of the 3-flows for which all periodic orbits and singularities are hyperbolic. This implies an extension of a result by Bowen (1976 Mixing Anosov flows Topology 15 77-9): C-1 robust transitive sets with singularities for generic flows in G(1)(M) are mixing. In particular, generic Lorenz attractors are transitive sets for their corresponding time-t map, t not equal 0.
引用
收藏
页码:359 / 378
页数:20
相关论文
共 17 条
[1]  
[Anonymous], PUBLICATIONS MATH IH
[2]   Creation of connections in C1-topology [J].
Arnaud, MC .
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (03) :211-214
[3]   MIXING ANOSOV FLOWS [J].
BOWEN, R .
TOPOLOGY, 1976, 15 (01) :77-79
[4]   PERIODIC ORBITS FOR HYPERBOLIC FLOWS [J].
BOWEN, R .
AMERICAN JOURNAL OF MATHEMATICS, 1972, 94 (01) :1-&
[5]  
DEMELO W, 1982, GEOMETRIC THEORY DYN
[6]   Connecting invariant manifolds and the solution of the C-1 stability and Omega-stability conjectures for flows [J].
Hayashi, S .
ANNALS OF MATHEMATICS, 1997, 145 (01) :81-137
[7]  
HAYASHI S, 2001, C1 MAKE BREAK LEMMA
[8]  
HAYASHI S, 1998, DOCUMENTA MATH, V2
[9]  
Hirsch M. W., 1977, LECT NOTES MATH, V583
[10]  
HU S, 1994, T AMS, V345, P730