Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers

• 成果类型: Article
• 署名作者: Morales, CA; Pacifico, MJ; Pujals, ER
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.160.375
• 发表日期: 2004
• 页码: 375-432
• 关键词: stability conjecture; invariant-manifolds; closing lemma; c-1 stability; diffeomorphisms; systems; FLOWS; density

摘要

Inspired by Lorenz' remarkable chaotic flow, we describe in this paper the structure of all C-1 robust transitive sets with singularities for flows on closed 3-manifolds: they are partially hyperbolic with volume-expanding central direction, and are either attractors or repellers. In particular, any C-1 robust attractor with singularities for flows on closed 3-manifolds always has an invariant foliation whose leaves are forward contracted by the flow, and has positive Lyapunov exponent at every orbit, showing that any C-1 robust attractor resembles a geometric Lorenz attractor.