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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.02622 |
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| _version_ | 1866910009666830336 |
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| author | Santos, Vaguiner Rodrigues dos Gabrick, Enrique Chipicoski Leonel, Edson Denis Caldas, Iberê Luiz |
| author_facet | Santos, Vaguiner Rodrigues dos Gabrick, Enrique Chipicoski Leonel, Edson Denis Caldas, Iberê Luiz |
| contents | In this work, we investigate scale invariance in the temporal evolution and chaotic regime of discrete dynamical systems. By exploiting the close interrelation between scaling and inversion transformations, we formulate scale symmetry in terms of inversion symmetry. As applications of our approach, we determine fractal dimensions and compute Lyapunov exponents for paradigmatic dynamical systems using scaling and inversion symmetries. By comparing our method with standard approaches, we obtain identical numerical values for the Lyapunov exponents using only a small number of iterations. Furthermore, our geometric-based framework naturally provides access to the fractal dimension. The agreement with standard results demonstrates that the proposed method is efficient and can be effectively employed in the study of dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02622 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrete dynamical systems with scaling and inversion symmetries Santos, Vaguiner Rodrigues dos Gabrick, Enrique Chipicoski Leonel, Edson Denis Caldas, Iberê Luiz General Physics In this work, we investigate scale invariance in the temporal evolution and chaotic regime of discrete dynamical systems. By exploiting the close interrelation between scaling and inversion transformations, we formulate scale symmetry in terms of inversion symmetry. As applications of our approach, we determine fractal dimensions and compute Lyapunov exponents for paradigmatic dynamical systems using scaling and inversion symmetries. By comparing our method with standard approaches, we obtain identical numerical values for the Lyapunov exponents using only a small number of iterations. Furthermore, our geometric-based framework naturally provides access to the fractal dimension. The agreement with standard results demonstrates that the proposed method is efficient and can be effectively employed in the study of dynamical systems. |
| title | Discrete dynamical systems with scaling and inversion symmetries |
| topic | General Physics |
| url | https://arxiv.org/abs/2602.02622 |