Dynamical fractalization of ring systems
Jerem\'ias Ruta, Nicol\'as Grandi, Tob\'ias Canavesi
TL;DR
This paper introduces an effective model for analyzing the dynamics of particles in circular ring systems, revealing stable configurations and fractal properties through continuum and statistical comparisons.
Contribution
It presents a novel effective modeling approach for particle ring dynamics and compares fractal dimensions with statistical Cantor systems.
Findings
Identifies stable configurations for various initial parameters.
Calculates fractal dimensions of the ring systems.
Shows similarities with Cantor set fractals.
Abstract
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for different initial parameters. We compute the resulting fractal dimension and compare it with that of a statistical Cantor ring system.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Fractional Differential Equations Solutions · Quantum chaos and dynamical systems