Year: 2025
Type: article
Abstract: We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from regularity to chaos. The systems are described by a two-dimensional, nonlinear mapping that preserves the area in the phase space. The key variables are the action and the angle, as usual from Hamiltonian systems. The transition is influenced by a control parameter giving the form of the order parameter. We observe a scaling invariance in the average squared action within the chaotic region, providing evidence that this change from regularity (integrability) to chaos (non-integrability) is akin to a second-order or continuous phase transition. As the order parameter approaches zero, its response against the variation in the control parameter (susceptibility) becomes increasingly pronounced (indeed diverging), resembling a phase transition.
Source: Entropy
DOI: 10.3390/e27080856
Author: Edson Denis Leonel
Institution: Universidade Estadual Paulista (Unesp)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4413181573