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Interaction of two charges in a uniform magnetic field: I. Planar problem
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Pinheiro, D. and MacKay, Robert S. (2006) Interaction of two charges in a uniform magnetic field: I. Planar problem. Nonlinearity, Vol.19 (No.8). pp. 1713-1745. doi:10.1088/0951-7715/19/8/002 ISSN 0951-7715.
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Official URL: http://dx.doi.org/10.1088/0951-7715/19/8/002
Abstract
The interaction of two charges moving in R-2 in a magnetic field B can be formulated as a Hamiltonian system with four degrees of freedom. Assuming that the magnetic field is uniform and the interaction potential has rotational symmetry we reduce this Hamiltonian system to one with two degrees of freedom; for certain values of the conserved quantities and choices of parameters, we obtain an integrable system. Furthermore, when the interaction potential is of the Coulomb type, we prove that, for suitable regimes of parameters, there are invariant subsets on which this system contains a suspension of a subshift of finite type. This implies non-integrability for this system with a Coulomb type interaction. Explicit knowledge of the reconstruction map and a dynamical analysis of the reduced Hamiltonian a description of the various types of dynamical behaviours in this system: from periodic to quasiperiodic and chaotic orbits, from bounded to unbounded motion.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Nonlinearity | ||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||
| ISSN: | 0951-7715 | ||||
| Official Date: | August 2006 | ||||
| Dates: |
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| Volume: | Vol.19 | ||||
| Number: | No.8 | ||||
| Number of Pages: | 33 | ||||
| Page Range: | pp. 1713-1745 | ||||
| DOI: | 10.1088/0951-7715/19/8/002 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Fundação para a Ciência e a Tecnologia (FCT) | ||||
| Grant number: | SFRH/BD/9239/2002 |
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