Entry and exit sets in the dynamics of area preserving Henon map

Abstract

In this paper we study dynamical properties of the area preserving Henon map, as a discrete version of open Hamiltonian systems, that can exhibit chaotic scattering. Exploiting its geometric properties we locate the exit and entry sets, i.e. regions through which any forward, respectively backward, unbounded orbit escapes to infinity. In order to get the boundaries of these sets we prove that the right branch of the unstable manifold of the hyperbolic fixed point is the graph of a function, which is the uniform limit of a sequence of functions whose graphs are arcs of the symmetry lines of the Henon map, as a reversible map.