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arXiv · 2602.01575

Templex-based dynamical units for a taxonomy of chaos

Caterina Mosto·Gisela D. Charó·Christophe Letellier·Denisse Sciamarella
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Abstract

Discriminating different types of chaos is still a very challenging topic, even for dissipative three-dimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to three-dimensional objects, since based on knot theory. To deal with higher-dimensional chaos, we recently introduced the templex combining a flow-oriented {\sc BraMAH} cell complex and a directed graph (a digraph). There is no dimensional limitation in the concept of templex. Here, we show that a templex can be automatically reduced into a ``minimal'' form to provide a comprehensive and synthetic view of the main properties of chaotic attractors. This reduction allows for the development of a taxonomy of chaos in terms of two elementary units: the oscillating unit (O-unit) and the switching unit (S-unit). We apply this approach to various well-known attractors (R\"ossler, Lorenz, and Burke-Shaw) as well as a non-trivial four-dimensional attractor. A case of toroidal chaos (Deng) is also treated. This work is dedicated to Otto E. R\"ossler.

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Caterina Mosto, Gisela D. Charó, Christophe Letellier, Denisse Sciamarella. 2026-02-02. Templex-based dynamical units for a taxonomy of chaos. https://doi.org/10.1063/5.0233160

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