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

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.