Transit Time in the Area-Preserving Hénon Maps

Chaotic solutions of unbounded area-preserving maps usually consist of an incoming regular path, a transitory irregular motion and a regular exit path. In simple situations the irregular motion occurs within a localized region of phase space and individual orbits do not access the whole chaotic domain. During its irregular portion an orbit spends a transient time wandering in a sub-region of the chaotic domain which is determined by its income path. We show that, for the area-preserving Hénon map, the transit time pattern is influenced by the distribution of intersections of invariant manifolds in the chaotic domain. To corroborate this assertion, we use an adaptive refinement procedure to obtain approximated sets of homoclinic and heteroclinic intersections. As the control parameter increases stickiness gets reduced and both homoclinic and heteroclinic sets have a similar distribution, indicating a transition to a more uniform type of transitory chaotic motion.