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Qualitative dynamics of potential systems on simply connected compact manifolds with ellipsoidal boundary in R 3

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Abstract

Potential systems on a simply connected compact manifold with ellipsoidal boundary in R3 are investigated in the present work for the case in which the potential of the system is an even forth-order symmetric polynomial. The sufficient conditions of the compact manifold boundary invariance are established. It is demonstrated that the interior punctured at the origin of coordinates is the region of compact manifold boundary attraction, and the qualitative dynamics is investigated.

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Authors and Affiliations

  1. Volgograd State University of Architecture and Building, Russia

    M. B. Belonenko & E. N. Ryzhov

Authors
  1. M. B. Belonenko
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  2. E. N. Ryzhov
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Correspondence to M. B. Belonenko.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 78–83, March, 2007.

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Belonenko, M.B., Ryzhov, E.N. Qualitative dynamics of potential systems on simply connected compact manifolds with ellipsoidal boundary in R 3 . Russ Phys J 50, 283–289 (2007). https://doi.org/10.1007/s11182-007-0039-y

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  • DOI: https://doi.org/10.1007/s11182-007-0039-y

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