Transactions of the American Mathematical Society

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On the reduction of dynamical systems by means of parametrized invariant relations


Authors: E. R. van Kampen and Aurel Wintner
Journal: Trans. Amer. Math. Soc. 44 (1938), 168-195
MSC: Primary 34A34; Secondary 34A25, 34C20, 37J15, 70F20, 70F25, 70H05
MathSciNet review: 1501966
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References [Enhancements On Off] (What's this?)

  • [1] F. Engel, Die Liesche Theorie der partiellen Differentialgleichungen erster Ordnung, edited by K. Faber, Leipzig, 1932.
  • [2] E. R. Van Kampen and Aurel Wintner, On the Canonical Transformations of Hamiltonian Systems, Amer. J. Math. 58 (1936), no. 4, 851–863. MR 1507207, 10.2307/2371255
  • [3] E. R. Van Kampen and Aurel Wintner, On a Symmetrical Canonical Reduction of the Problem of Three Bodies, Amer. J. Math. 59 (1937), no. 1, 153–166. MR 1507227, 10.2307/2371569
  • [4] T. Levi-Civita, Sur la recherche des solutions particulières des systèmes différentiels et sur les mouvements stationaires, Prace Matematyczno-Fizyczne, vol. 17 (1906), pp. 1-40.
  • [5] T. Levi-Civita, Sulla introduzione di vincoli olonomi nelle equazioni dinamiche di Hamilton Atti del Reale Istituto Veneto, (8), vol. 18$ _{1}$ (1916), pp. 387-395.
  • [6] Aurel Wintner, On the linear conservative dynamical systems, Ann. Mat. Pura Appl. 13 (1934), no. 1, 105–112. MR 1553236, 10.1007/BF02413437

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DOI: http://dx.doi.org/10.1090/S0002-9947-1938-1501966-6
Article copyright: © Copyright 1938 American Mathematical Society