The fractal invariant measure of chaotic strange attractors can be approximated systematically by the set of unstable n-periodic orbits of increasing n. Algorithms for extracting the periodic orbits from a chaotic time series and for calculating their stabilities are presented. With this information alone, important properties like the topological entropy and the Hausdorff dimension can be calculated.

• Received 13 March 1987

DOI:https://doi.org/10.1103/PhysRevLett.58.2387