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II Genus-oneattractors with multiple unimodalfolding mechanisms Martin Rosalie & Christophe Letellier In a recent paper, we proposed a systematic procedure to extract template for genus-one chaotic attractors with a single folding mechanism, that is, for attractor bounded by a genus-one torus [1, 2] and characterized by a unimodal smooth
A representation of a template of a chaotic attractor solution to the Malasoma system (1) for α = 2.027. (a) Chaotic attractor with the Poincaré section (see  for the definition of this section...
This multiplicative law that we will introduce in this paper appears as the required companion to the additive law introduced in our previous work [ 3] to develop a systematic procedure for extracting templates for attractors with multiple foldings. The present work concerns attractors bounded by genus-one tori.
Systematictemplateextractionfromchaotic attractors. II 2 1. Introduction In a recent paper, we proposed a systematic procedure to extract template for genus-
Asymmetric and symmetric chaotic attractors produced by the simplest jerk equivariant system are topologically characterized. In the case of this system with an inversion symmetry, it is shown that symmetric attractors bounded by genus-one tori are conveniently analyzed using a two-components Poincare section. Resulting from a merging attractor crisis, these attractors can …
Figure 1. (Color online) Coexisting asymmetric attractors, A (black) andA (red) solution to system (1) and issued from two symmetric sets of initial conditions. Parameter value α = 2.0645. - "Systematic template extraction from chaotic attractors: II. Genus-one attractors with multiple unimodal folding mechanisms"
Systematic Template Extraction From Chaotic Attractors: II. Genus-One Attractors With Multiple Unimodal Folding Mechanisms by Martin Rosalie, ... Systematic Template Extraction From Chaotic Attractors: II. Genus-One Attractors With Multiple Unimodal Folding Mechanisms Journal of Physics A: Mathematical and Theoretical - United …
A template or a branched manifold is a branched surface that synthesizes the topology of an attractor by describing the relative organisation of the population of unstable periodic orbits  which constitutes the skeleton of the attractor . Any template for a chaotic attractor bounded by a genus-one torus can be divided in two main