| Abstrakt: |
Let X be a C vector field on a compact boundaryless Riemannian manifold M (dim M ≥ 2), and Λ a compact invariant set of X. Suppose that Λ has a hyperbolic splitting, i.e., T M = E ⊕〈 X〉⊕ E with E uniformly contracting and E uniformly expanding. We prove that if, in addition, Λ is chain transitive, then the hyperbolic splitting is continuous, i.e., Λ is a hyperbolic set. In general, when Λ is not necessarily chain transitive, the chain recurrent part is a hyperbolic set. Furthermore, we show that if the whole manifold M admits a hyperbolic splitting, then X has no singularity, and the flow is Anosov. [ABSTRACT FROM AUTHOR] |
Full text from SpringerLink