An Application of Computational Topology to Dynamical Systems
by
Vanessa Robins
University of Colorado
Coauthors: James D. Meiss (University of Colorado), Elizabeth Bradley (University of Colorado)

We present computational techniques that detect bifurcations in the topology of invariant sets. A familiar example comes from 2-d area-preserving twist maps. Invariant circles trap chaotic orbits and imply some degree of stability that is destroyed when the nonlinearity is increased. Analogous structures in higher-dimensional maps are difficult to visualize so computational tools are necessary to give quantitative information about their topology. In particular, we characterize how the number of components and number of holes vary with a resolution parameter.

Date received: June 7, 1999