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• W2018209945 abstract "The interaction of two charges moving in 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 systems are the tools we use in order to give a description of the various types of dynamical behaviours in this system: from periodic to quasiperiodic and chaotic orbits, from bounded to unbounded motion." @default.
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• W2018209945 date "2006-06-29" @default.
• W2018209945 modified "2023-09-23" @default.
• W2018209945 title "Interaction of two charges in a uniform magnetic field: I. Planar problem" @default.
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• W2018209945 doi "https://doi.org/10.1088/0951-7715/19/8/002" @default.
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