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Global relativistic effects in chaotic scattering.

Juan D Bernal1, Jesús M Seoane1, Miguel A F Sanjuán1,2

  • 1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.

Physical Review. E
|April 19, 2017
PubMed
Summary

This study explores relativistic chaotic scattering in the Hénon-Heiles system. Increasing relativistic factor β decreases escape time and alters decay laws, revealing a scaling relationship.

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Area of Science:

  • Physics
  • Astrophysics
  • Nonlinear Dynamics

Background:

  • Chaotic scattering is crucial in science and engineering.
  • Previous studies focused on Newtonian mechanics with low particle velocities.
  • Relativistic effects on chaotic systems remain less explored.

Purpose of the Study:

  • Analyze global properties of the Hénon-Heiles system under special relativity.
  • Investigate escape time distribution and decay laws in a relativistic context.
  • Examine the influence of the relativistic factor (β) on chaotic dynamics.

Main Methods:

  • Numerical simulations of the Hénon-Heiles system.
  • Analysis of escape time distributions.
  • Study of survival probability and decay laws.

Related Experiment Videos

  • Investigation of phase space structures (KAM islands).

    • Main Results:

    • Average escape time decreases as relativistic factor β increases.
    • KAM islands are destroyed at β≃0.4, indicating a transition in dynamics.
    • Survival probability exhibits algebraic decay for β≤0.4 and exponential decay for β>0.4.
    • A surprising quadratic scaling law is found between the decay exponent and β.

    Conclusions:

    • Relativistic effects significantly alter chaotic scattering dynamics.
    • The Hénon-Heiles system shows a clear transition in behavior at a critical relativistic factor.
    • The discovered scaling law offers new insights into relativistic chaotic systems.