Alternative determinism principle for topological analysis of chaos

Alternative determinism principle for topological analysis of chaos

The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proven to be 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-...

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Veröffentlicht in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2006-09, Vol.74 (3 Pt 2), p.035202-035202, Article 035202
1. Verfasser: Lefranc, Marc
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Sprache:eng
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Chaotic Dynamics
Nonlinear Sciences
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description The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proven to be 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 we show that in dimension 3 our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.
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Nonlinear Sciences
title Alternative determinism principle for topological analysis of chaos
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