Templex-based dynamical units for a taxonomy of chaos
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918318602977280 |
|---|---|
| author | Mosto, Caterina Charó, Gisela D. Letellier, Christophe Sciamarella, Denisse |
| author_facet | Mosto, Caterina Charó, Gisela D. Letellier, Christophe Sciamarella, Denisse |
| contents | 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 (Rössler, 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. Rössler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01575 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Templex-based dynamical units for a taxonomy of chaos Mosto, Caterina Charó, Gisela D. Letellier, Christophe Sciamarella, Denisse Chaotic Dynamics 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 (Rössler, 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. Rössler. |
| title | Templex-based dynamical units for a taxonomy of chaos |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2602.01575 |