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

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

2002-09-23

arxiv.org/abs/nlin/0209046v1

Chaos, Solitons and Fractals 17 (2003) 651-658

Nonlinear Sciences

Chaotic Dynamics

12 pages, Latex2e, four ps figures

Scientific paper

10.1016/S0960-0779(02)00475-7

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.

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