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Chaos and regularity in an anisotropic soft squircle billiard
A González Andrade1, H N Núñez-Yépez1, M A Bastarrachea-Magnani1
1Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, C.P. 09310 CDMX, México.
Physical Review. E
|January 21, 2026
Summary
This study explores the anisotropic soft-wall squircle billiard, revealing how its parameters influence chaotic dynamics and regular behavior. Understanding these transitions enhances our knowledge of soft billiard systems.
Area of Science:
- Mathematical Physics
- Dynamical Systems Theory
Background:
- Hard-wall billiards model particle confinement with instantaneous collisions.
- Soft billiards generalize this with smooth boundaries governed by Hamiltonian dynamics, offering more realistic models.
Purpose of the Study:
- To investigate the dynamical features of an anisotropic soft-wall squircle billiard.
- To characterize the transition from regular to chaotic trajectories within this system.
Main Methods:
- Analysis of trajectories in a novel anisotropic soft-wall squircle billiard.
- Computation of Poincaré surfaces of section.
- Calculation of Lyapunov exponents across parameter space.
Main Results:
- Demonstration of the onset of chaos and its alternation with regular dynamics.
- Characterization of the transition to chaos and dynamic stabilization.
- Revealed nonlinearity of squareness, ellipticity, and hardness parameters.
Conclusions:
- The anisotropic soft-wall squircle billiard exhibits complex dynamics with transitions to chaos.
- Poincaré sections and Lyapunov exponents effectively characterize these dynamical regimes.
- This work provides a tool for understanding chaos onset in soft billiards.
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