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Lie symmetries of generalized Ermakov systems

  • Dynamical Systems
  • Conference paper
  • First Online:
Dynamical Systems, Plasmas and Gravitation

Part of the book series: Lecture Notes in Physics ((LNP,volume 518))

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Abstract

The Lie point symmetry analysis of Ermakov systems is extended to the case where the frequency function in the equations of motion depends also on the dynamical variables and their derivatives. From this new standpoint, a quite general class of two dimensional oscillators with nonlinear coupling can be viewed as a Hamiltonian Ermakov system possessing a Lie point symmetry and is shown to be completely integrable.

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Authors and Affiliations

  1. Instituto de Física-UFRGS, Caixa Postal 15051, 91500-970, Porto Alegre, RS, Brazil

    Fernando Haas & Joao Goedert

Authors
  1. Fernando Haas
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  2. Joao Goedert
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Editor information

P. G. L. Leach S. E. Bouquet J.-L. Rouet E. Fijalkow

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© 1999 Springer-Verlag

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Haas, F., Goedert, J. (1999). Lie symmetries of generalized Ermakov systems. In: Leach, P.G.L., Bouquet, S.E., Rouet, JL., Fijalkow, E. (eds) Dynamical Systems, Plasmas and Gravitation. Lecture Notes in Physics, vol 518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105933

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  • DOI: https://doi.org/10.1007/BFb0105933

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65467-4

  • Online ISBN: 978-3-540-49251-1

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