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Toward a General Procedure for Extracting Templates from Chaotic Attractors Bounded by High Genus Torus

CORIA-UMR 6614–Normandie Université, CNRS–Université et INSA de Rouen, Campus Universitaire du Madrillet, 76800 Saint-Etienne-du-Rouvray, France

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Christophe Letellier

CORIA-UMR 6614–Normandie Université, CNRS–Université et INSA de Rouen, Campus Universitaire du Madrillet, 76800 Saint-Etienne-du-Rouvray, France

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https://doi.org/10.1142/S021812741450045XCited by:10 (Source: Crossref)

Abstract

The topological analysis of chaotic attractor by means of template is rather well established for simple attractors as solution to the Rössler system. Lorenz-like attractors are already slightly more complicated because they are bounded by a genus-3 bounding torus, implying the necessity to use a two-component Poincaré section. In this paper, we enriched the concept of linking matrix to correctly describe an algebraic template for an attractor with (g - 1) components of Poincaré section and whose bounding torus has g interior holes aligned. An example with g = 5 — a multispiral attractor — is explicitly treated.

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