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On Holomorphic Solutions of the Darwin Equations of Motion of Point Charges

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Ukrainian Mathematical Journal Aims and scope

The existence of holomorphic (in time) solutions of the nonrelativistic Darwin equations of motion of point charges is proved with the help of the Cauchy theorem.

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References

  1. E. T. Wittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Univ. Press, Cambridge (1927).

    Google Scholar 

  2. L. D. Landau and E. M. Lifshits, Field Theory [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  3. H.-J. Treder, Die Relativitat der Tragheit, Academie, Berlin (1972).

    Google Scholar 

  4. M. Kunze and H. Spohn, Slow Motion of Charges Interacting Through the Maxwell Field, Prepint, arXiv: math-phys/0001002v1, 3 January.

  5. W. I. Skrypnyk, “On the holomorphic solutions of Hamiltonian equations of motion of point charges,” Ukr. Mat. Zh., 63, No. 2, 270–280 (2011); English translation: Ukr. Math. J., 63, No. 2, 315–327 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  6. C. L. Siegel and J. K. Moser, Lectures on Celestial Mechanics, Springer, Berlin (1971).

    Book  MATH  Google Scholar 

  7. V. V. Golubev, Lectures on the Analytic Theory of Differential Equations [in Russian], Akad. Nauk SSSR, Moscow (1950).

    Google Scholar 

  8. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York (1955).

    MATH  Google Scholar 

  9. D. K. Faddeev, Lectures on Algebra [in Russian], Nauka, Moscow (1984).

    Google Scholar 

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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. 65, No. 4, pp. 546–554, April, 2013.

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Skrypnyk, W.I. On Holomorphic Solutions of the Darwin Equations of Motion of Point Charges. Ukr Math J 65, 602–611 (2013). https://doi.org/10.1007/s11253-013-0798-2

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  • DOI: https://doi.org/10.1007/s11253-013-0798-2

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