Integrability of magnetic fields created by current distributions
Jacobo AguirreCentro de Astrobiología, CSIC-INTA, Ctra. Ajalvir, Km. 4, 28850 Torrejón de Ardoz, SpainJaume GinéDepartament de Matemàtica, Universitat de Lleida, Avda Jaume II 69, 25001 Lleida, SpainDaniel Peralta‐SalasDepartamento de Matemáticas, Universidad Carlos III, Avda Universidad, 30, 28911 Leganés, Spain
2007en
ABI
Abstract
The existence of first integrals and periodic orbits of magnetic fields created by thin wires is investigated. When the current lines are planar we prove that magnetic orbits are closed near the wires and we provide two examples of magnetic fields without polynomial first integrals, thus contradicting Stefanescu's conjecture. When the current lines are non-planar we provide some examples of rectilinear configurations giving rise to helicoidal orbits near the wires and to chaotic portraits.
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Cited by 20 references