Symbolic Dynamics of Magnetic Bumps

TL;DR

This paper constructs a complete symbolic dynamics model for a classical particle moving at constant speed within a plane containing multiple convex magnetic bumps, under specific curvature and magnetic field conditions.

Contribution

It introduces a novel symbolic dynamics framework for particle motion in magnetic bump configurations with particular geometric and magnetic constraints.

Findings

Established a symbolic coding for particle trajectories

Demonstrated the model's completeness for the specified system

Provided insights into the dynamics of particles in magnetic bump fields

Abstract

For n convex magnetic bumps in the plane, whose boundary has a curvature somewhat smaller than the absolute value of the constant magnetic field inside the bump, we construct a complete symbolic dynamics of a classical particle moving with speed one.