Nonlinear Phenomena in Complex Systems, 2010, Vol.13, No.1, pp.79-84

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2010, Vol.13, No.1, pp.79-84

Nonlinear Dynamics of Magnetic Field Lines.
T. Miyaguchi, M. Hosoda, K. Imagawa, and K. Nakamura

Nonlinear dynamics of magnetic field lines generated by simple electric current elements are investigated. In general, the magnetic field lines show behavior similar to that of the Hamiltonian systems; in fact, they can be generally transformed into 1.5 degrees of freedom Hamiltonian systems and obey the KAM theorem. In the case where unperturbed systems are described by two action (slow) and one angle (fast) variables, however, it is found that the periodic orbits of the unperturbed systems vanish for arbitrarily small symmetry-breaking perturbations (a breakdown of the KAM theorem). The mechanism of this phenomenon is investigated by weak nonlinear stability analysis.
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