Nonsingular star flows satisfy axiom a and the no-cycle condition

• 成果类型: Article
• 署名作者: Gan, SB; Wen, L
• 署名单位: Peking University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0479-3
• 发表日期: 2006
• 页码: 279-315
• 关键词: c-1 stability conjecture; homoclinic tangencies; PROOF; diffeomorphisms; systems; sets

摘要

We give an affirmative answer to a problem of Liao and Mane which asks whether, for a nonsingular flow to loose the Omega-stability, it must go through a critical-element-bifurcation. More precisely, a vector field S on a compact boundaryless manifold is called a star system if S has a C-1 neighborhood U in the set of C-1 vector fields such that every singularity and every periodic orbit of every X epsilon U is hyperbolic. We prove that any nonsingular star flow satisfies Axiom A and the no cycle condition.