Partial Lyapunov stability and partial Lipschitz stability in Flows are introduced. It is proved that a flow on a compact metric space is Lyapunov stable if and only if it is partial Lyapunov stable with respect to a ...Partial Lyapunov stability and partial Lipschitz stability in Flows are introduced. It is proved that a flow on a compact metric space is Lyapunov stable if and only if it is partial Lyapunov stable with respect to a c -dense subset of the real numbers. Also it is proved that a C r(r≥ 1) flow on a compact, connected Riemannian manifold is Lipschitz stable if and only if it is partial Lipschitz stable with respect to a c -dense subset of the real numbers. Moreover, the dynamical properties of transitive Lyapunov stable flows are studied.展开更多
文摘Partial Lyapunov stability and partial Lipschitz stability in Flows are introduced. It is proved that a flow on a compact metric space is Lyapunov stable if and only if it is partial Lyapunov stable with respect to a c -dense subset of the real numbers. Also it is proved that a C r(r≥ 1) flow on a compact, connected Riemannian manifold is Lipschitz stable if and only if it is partial Lipschitz stable with respect to a c -dense subset of the real numbers. Moreover, the dynamical properties of transitive Lyapunov stable flows are studied.
