Alternative determinism principle for topological analysis of chaos

Details Alternative determinism principle for topological analysis of chaos Alternative determinism principle for topological analysis of chaos

2005-03-04

arxiv.org/abs/nlin/0503006v3

Physical Review E 74 (2006) 035202

Nonlinear Sciences

Chaotic Dynamics

Accepted for publication as Rapid Communication in Physical Review E

Scientific paper

10.1103/PhysRevE.74.035202

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.

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