Chaotic Dynamics of Charged Particles in Magnetic Fields with Singular Forces
Abstract
We study charged-particle dynamics under a non-Lipschitz velocity-dependent force with magnetic and damping effects, focusing on continuation through zero velocity and chaos in the velocity direction. For a time-independent directional force and fixed parameters, we introduce a C1 regularization. When an unregularized trajectory reaches zero velocity in finite time, inner rescaling yields convergence to a reference orbit within the regularization ball, while the regularized trajectories converge locally uniformly outside it to a unique continuation. For the directional dynamics, stereographic projection yields a parameterized Euclidean system. By choosing the skew-symmetric magnetic part, we obtain a nonautonomous parameterized center manifold reduction with a prescribed finite Taylor jet. Under an additional factorization assumption, the reduced dynamics admits Shilnikov homoclinic orbits and associated chaos.
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BibTeX
@misc{chen2026chaotic,
title = {{Chaotic Dynamics of Charged Particles in Magnetic Fields with Singular Forces}},
author = {Linhao Chen and Yong Li and Weiping Yan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01699},
eprint = {2611.01699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01699},
}
RIS
TY - UNPB
TI - Chaotic Dynamics of Charged Particles in Magnetic Fields with Singular Forces
AU - Linhao Chen
AU - Yong Li
AU - Weiping Yan
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01699
UR - https://arxiv.org/abs/2611.01699
AB - We study charged-particle dynamics under a non-Lipschitz velocity-dependent force with magnetic and damping effects, focusing on continuation through zero velocity and chaos in the velocity direction. For a time-independent directional force and fixed parameters, we introduce a C^1 regularization. When an unregularized trajectory reaches zero velocity in finite time, inner rescaling yields convergence to a reference orbit within the regularization ball, while the regularized trajectories converge locally uniformly outside it to a unique continuation. For the directional dynamics, stereographic projection yields a parameterized Euclidean system. By choosing the skew-symmetric magnetic part, we obtain a nonautonomous parameterized center manifold reduction with a prescribed finite Taylor jet. Under an additional factorization assumption, the reduced dynamics admits Shilnikov homoclinic orbits and associated chaos.
ER -