Topological aspects of chaotic scattering in higher dimensions - art. no. 056207

We investigate the topological properties of the chaotic invariant set asso ciated with the dynamics of scattering systems with three or more degrees o f freedom. We show that the separation of one degree of freedom from the re st in the asymptotic regime, a common property in a large class of scatteri ng models, defines a gate which is a dynamical object with phase space sepa rating invariant manifolds. The manifolds form an invariant set causing sin gularities in the scattering process. The codimension one property of the m anifolds ensures that the fractal structure of the invariant set can be stu died by scattering functions defined over simple one-dimensional families o f initial conditions as usually done in two-degree-of-freedom scattering pr oblems. It is found that the fractal dimension of the invariant set is not due to the gates but to interior hyperbolic periodic orbits.