Stability of hyperbolic vector fields

摘要

We giue a geometrical proof of the global stability theorem for a large class of hyperbolic vector fields (i.e. those satisfying axiom A and the strong transversality condition). The class of hyperbolic vector fields we consider in this paper is constituted by those hyperbolic vector fields for which the attractor and repellor sets are trivial (i.e. sigularities and/or periodic orbits) and their non-trivial basic sets are d-separated.