Symmetry breaking: A tool to unveil the topology of chaotic scattering with three degrees of freedom

TL;DR

This paper explores how symmetry breaking can be used to understand the complex topology of chaotic scattering systems with three degrees of freedom, focusing on the structure of invariant sets and scattering functions.

Contribution

It introduces a novel approach using symmetry breaking to analyze the topology of chaotic scattering with more than two degrees of freedom.

Findings

Characterizes the homoclinic/heteroclinic tangle structure.

Links chaotic invariant sets to scattering functions.

Identifies singularities in the scattering cross section.

Abstract

We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.