2005/03/31 by Marc Lefranc · 1 citation
Physics and Astronomy · #nlin.CD
paper · pdf · doi:10.1103/physreve.74.035202
published as Physical Review E 74 (2006) 035202 · Accepted for publication as Rapid Communication in Physical Review E
arxiv created 2006/08/31 · arxiv updated 2009/12/01
The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.