Coupled Arnol'd cat maps on circulant graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910244461871104 |
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| author | Manolas, Kimon Floratos, Emmanuel |
| author_facet | Manolas, Kimon Floratos, Emmanuel |
| contents | This paper investigates the chaotic properties of Arnol'd cat maps (ACMs) coupled on the nodes of a circulant graph. By demanding that the system's evolution matrix be symplectic, we determine the coupling matrix, which is naturally interpreted as the adjacency matrix of a circulant graph. Specifically, the study analyses the system's Lyapunov spectra and Kolmogorov-Sinai (K-S) entropy. Numerical simulations yield the counterintuitive result that the entropy production does not increase as the connectivity of the graph increases, due to the translational symmetry of the circulant graph. Moreover, we analyse the spectra of the periods of the evolution matrix on a finite toroidal phase space of the dynamical system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coupled Arnol'd cat maps on circulant graphs Manolas, Kimon Floratos, Emmanuel Dynamical Systems High Energy Physics - Theory Chaotic Dynamics This paper investigates the chaotic properties of Arnol'd cat maps (ACMs) coupled on the nodes of a circulant graph. By demanding that the system's evolution matrix be symplectic, we determine the coupling matrix, which is naturally interpreted as the adjacency matrix of a circulant graph. Specifically, the study analyses the system's Lyapunov spectra and Kolmogorov-Sinai (K-S) entropy. Numerical simulations yield the counterintuitive result that the entropy production does not increase as the connectivity of the graph increases, due to the translational symmetry of the circulant graph. Moreover, we analyse the spectra of the periods of the evolution matrix on a finite toroidal phase space of the dynamical system. |
| title | Coupled Arnol'd cat maps on circulant graphs |
| topic | Dynamical Systems High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2605.00965 |