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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.
Physical Review. E
|July 22, 2020
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.
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.
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