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On the holomorphic solutions of Hamiltonian equations of motion of point charges

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Ukrainian Mathematical Journal Aims and scope

The Maxwell–Lorenz system of electromagnetic fields interacting with charged particles (point charges) is studied in the Darwin approximation in which the Lagrangian and Hamiltonian of the particles are not coupled with the field. The solution of the equation of motion of particles with approximate Darwin Hamiltonian is found in a finite time interval by using the Cauchy theorem. The components of this solution are represented as holomorphic functions of time.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    W. I. Skrypnyk

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  1. W. I. Skrypnyk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 2, pp. 270–280, February, 2011.

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Skrypnyk, W.I. On the holomorphic solutions of Hamiltonian equations of motion of point charges. Ukr Math J 63, 315–327 (2011). https://doi.org/10.1007/s11253-011-0505-0

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  • DOI: https://doi.org/10.1007/s11253-011-0505-0

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