Connecting the spatial structure of periodic orbits and invariant manifolds in hyperbolic area-preserving systems

Abstract

This Letter discusses the equivalence between the Bowen measure associated with the set Per ( n ) of periodic points of period n of hyperbolic area-preserving maps of a smooth manifold, and the measure associated with the intersections between stable and unstable manifolds of hyperbolic points. In typical cases of physical interest (i.e., nonuniformly hyperbolic systems) these measures are found to be highly nonuniform (multifractal).