Topological aspects of the structure of chaotic attractors in R3.

摘要

We extend the methods for topological analysis of chaotic dynamical systems in R3 by introducing two new concepts---embedding manifolds and their canonical forms. These are used to specify in topological terms the large scale global structure of chaotic attracting sets. We show how these ideas help us put the finishing touch on the third coarsest level in a classification scheme for strange attractors in R3 , for which the two lower levels have been constructed about a decade ago. In addition we present a guide on how to construct a Poincare surface of section for strange attractors with Lyapunov dimension dL 3. We show how to extract information about the canonical form from scalar time series. In addition we discuss what possible changes occur to the topological properties of the unstable periodic orbits in the strange attractor, as we use different embedding mappings into R3 .