Positive topological entropy for multi-bump magnetic fields

TL;DR

This paper demonstrates that a charged particle moving in a planar magnetic field with multiple localized peaks exhibits complex dynamics with positive topological entropy, indicating chaotic behavior.

Contribution

It establishes that such magnetic field configurations are semi-conjugate to a full shift on multiple symbols, revealing new insights into their chaotic dynamics.

Findings

System has positive topological entropy

Dynamics are semi-conjugate to a full shift on n symbols

Chaotic behavior under mild geometric conditions

Abstract

We study the dynamics of a charged particle in a planar magnetic field which consists of $n\geq 2$ disjoint localized peaks. We show that, under mild geometric conditions, this system is semi-conjugated to the full shift on $n$ symbols and, hence, carries positive topological entropy.