Discrete dynamical systems with scaling and inversion symmetries
Abstract
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.
Cite
@article{arxiv.2602.02622,
title = {Discrete dynamical systems with scaling and inversion symmetries},
author = {Vaguiner Rodrigues dos Santos and Enrique Chipicoski Gabrick and Edson Denis Leonel and Iberê Luiz Caldas},
journal= {arXiv preprint arXiv:2602.02622},
year = {2026}
}