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Transient chaos under coordinate transformations in relativistic systems.

D S Fernández1, Á G López1, J M Seoane1

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

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Summary

This study explores relativistic effects on chaotic scattering using the Hénon-Heiles system. Transient chaotic dynamics and time dilation are shown to be invariant across reference frames, demonstrating coordinate independence.

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Area of Science:

  • Physics
  • Dynamical Systems
  • Chaos Theory

Background:

  • The Hénon-Heiles system is a standard model for studying chaotic scattering.
  • Understanding transient chaos and relativistic effects is crucial in physics.

Purpose of the Study:

  • To investigate the influence of Lorentz factor on transient chaotic dynamics.
  • To analyze time dilation within the scattering region using a particle-attached clock.
  • To determine the relativistic invariance of chaotic scattering phenomena.

Main Methods:

  • Utilizing the Hénon-Heiles system as a model for chaotic scattering.
  • Measuring time dilation effects with a comoving clock.
  • Analyzing escape time functions and their singularities.
  • Employing a Cantor-like set approach and the uncertainty dimension algorithm.

Main Results:

  • Time dilation events exhibit sensitivity to initial conditions.
  • Singularities in the escape time function are invariant under coordinate transformations.
  • The fractal dimension of the escape time function is relativistically invariant.
  • Fractal dimensions computed in inertial and comoving frames are consistent.

Conclusions:

  • Chaotic transient phenomena are mathematically predictable in any reference frame.
  • Transient chaos demonstrates coordinate invariance, irrespective of the observer's frame.