Chaotic dynamics on a strange attractor of low dimensionality can be characterized by a set of recently proposed topological invariants. These are the relative rotation rates of the unstable periodic orbits embedded in the strange attractor. We demonstrate the efficiency of this characterization by extracting the topological invariants from chaotic time-series data for the Duffing oscillator.

• Received 16 March 1990

DOI:https://doi.org/10.1103/PhysRevA.41.5717