Transient Chaos in Dissipative Chaotic Scattering

Abstract

In this thesis we consider the influence of dissipative effects on dynamical systems whose unperturbed dynamics are already transiently chaotic. The class of systems we study have been used to model a wide range of physical processes, from celestial-mechanical motions to hydrodynamic flows, which are susceptible to such perturbations. We use existing theory on transient chaos and powerful numerical methods to gain a comprehensive understanding of the dynamics of these scattering systems in both conservative and dissipative settings, in terms of macroscopic quantities like the survival rate of trajectories in particular phase space regions, or the fractal scaling of basin boundaries between final states. We then propose a general framework, inspired by earlier work on pullback attractors, for understanding the qualitative differences and general phenomenology visible in the numeri cal results for the dissipative system. In particular, we find that features related to conditionally-invariant measures of the unperturbed system can be used to explain the observations of the dissipative system, even when the dynamics of each case are substantially different.