Topological aspects of chaotic scattering in higher dimensions

Details Topological aspects of chaotic scattering in higher dimensions Topological aspects of chaotic scattering in higher dimensions

1998-09-30

arxiv.org/abs/chao-dyn/9810006v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 4 figures in 5 GIF files

Scientific paper

We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the asymptotic regime, a common property in a large class of scattering models, defines a dynamical object with phase space separating invariant manifolds and an invariant set with larger dimension than that of the set defined by bounded orbits. In particular, the set of typical periodic orbits involving all the degrees of freedom of the system form a nowhere dense subset of the large invariant set.

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