Mixing attractors for 3-flows

Citation
Ca. Morales et Mj. Pacifico, Mixing attractors for 3-flows, NONLINEARIT, 14(2), 2001, pp. 359-378
Citations number
17
Categorie Soggetti
Mathematics
Journal title
NONLINEARITY
ISSN journal
09517715 → ACNP
Volume
14
Issue
2
Year of publication
2001
Pages
359 - 378
Database
ISI
SICI code
0951-7715(200103)14:2<359:MAF3>2.0.ZU;2-G
Abstract
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 sin gularities 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, gene ric Lorenz attractors are transitive sets for their corresponding time-t ma p, t not equal 0.