Classification of strange attractors by integers

Abstract

We show how to characterize a strange attractor by a set of integers. These are extracted from the chaotic time-series data by first reconstructing the low-period orbits and then determining the template, or knot holder, which supports all periodic orbits embedded in the strange attractor, and the strange attractor itself. The template is identified by a set of integers which therefore characterize the strange attractor. This identification is explicitly demonstrated for the Pirogon using a relatively small data set (5000 points).