Local structural stability of actions of R^n on n-manifolds

Boletim da Sociedade Paranaense de Matemática

关键词: Group action;    singular orbit;    hyperbolicity;    structural stability.;   

DOI  :  

来源: DOAJ

【 摘 要 】

Let M^m be a compact m-manifold and ϕ:R^n × M^m → M^m a C^r, r ≥ 1, action with infinitesimal generators of class C^r . We introduce theconcept of transversally hyperbolic singular orbit for an action ϕ and explore this concept in its relations to stability. Our main result says that if m = n and O_p is a compact singular orbit of ϕ that is transversally hyperbolic, then ϕ is C^1 locally structurally stable at O_p .

【 授权许可】

Unknown