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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2006

Alternative determinism principle for topological analysis of chaos

Résumé

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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Dates et versions

hal-00004359 , version 1 (04-03-2005)
hal-00004359 , version 2 (19-05-2005)
hal-00004359 , version 3 (31-08-2006)

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Marc Lefranc. Alternative determinism principle for topological analysis of chaos. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2006, 74, pp.035202(R). ⟨10.1103/PhysRevE.74.035202⟩. ⟨hal-00004359v3⟩
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