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Pré-Publication, Document De Travail Année : 2005

Alternative determinism principle for topological analysis of chaos

Résumé

The topological analysis of deterministic 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. As a first step toward a formalism applicable in higher dimensions, we show that in dimension three our approach 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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Citer

Marc Lefranc. Alternative determinism principle for topological analysis of chaos. 2005. ⟨hal-00004359v2⟩
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