COUNTING LOW-PERIOD CYCLES FOR FLOWS

Abstract

In this paper we describe a rigorous method to find for a continuous system all low-period cycles enclosed in a certain region of the state space. As an example of the application of this technique we present the complete analysis of the Rössler attractor in terms of short periodic orbits. We construct the trapping region for the associated Poincaré map. The trapping region encloses the numerically observed attractor. We find all periodic orbits of the Poincaré map up to period 20. We prove that these periodic orbits correspond to all cycles of the flow with period shorter than 120. Using the number of short periodic orbits we compute estimates for topological entropy of the Poincaré map and the flow.