We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stabl...We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms.For example,we can then show tha t a bi-Lyapunov st able homoclinic class for a C^(1)generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.展开更多
文摘We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms.For example,we can then show tha t a bi-Lyapunov st able homoclinic class for a C^(1)generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.
