Newtonian vs. relativistic chaotic scattering

TL;DR

This paper compares Newtonian and relativistic mechanics in chaotic scattering, showing Newtonian mechanics is inadequate for individual trajectories at low velocities but can still accurately predict some global properties of the system.

Contribution

It demonstrates the limitations of Newtonian mechanics for individual trajectories in slow chaotic scattering while confirming its effectiveness for global system properties.

Findings

Newtonian mechanics fails for individual trajectories at low velocities.

Global properties like the dimension of chaotic sets are reliably estimated by Newtonian approximation.

Relativistic effects are significant for accurate trajectory predictions in chaotic scattering.

Abstract

It is shown that Newtonian mechanics is not appropriate to compute approximate individual trajectories with small velocities in chaotic scattering. However, some global properties of the dynamical system, such as the dimension of the non-attracting chaotic invariant set, are more robust and the Newtonian approximation provides reasonably accurate results for them in slow chaotic scattering.