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The 1:2:1-resonance, its periodic orbits and integrals

Part of the Lecture Notes in Mathematics book series (LNM,volume 711)

Keywords

  • Periodic Solution
  • Periodic Orbit
  • Normal Form
  • Quadratic Part
  • Stability Type

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References

  1. Abraham, R: Foundations of Mechanics, Benjamin, Reading, Mass. (1967).

    Google Scholar 

  2. Birkhoff, G.D.: Dynamical Systems, Am. Math. Soc. (1927).

    Google Scholar 

  3. Cushman, R.: The Momentum Mapping of the Harmonic Oscillator, Instituto Nazionale di Alta Matematica, Symposia Mathematica, Vol XIV (1974).

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  4. Mei, C.C. and Unlüata, U.: Harmonic Generation in Shallow Water Waves, in: Waves and Beaches, Ed. R.E. Meyer, Publ. no. 28 Math. Res. Center, Univ. Wisconsin, Ac. Press, N.Y. (1972).

    Google Scholar 

  5. Sanders, J.A.: Are Higher Order Resonances Really Interesting? Celestial Meachanics 16 (1978) 421–440.

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  6. Siegel, C.L. and Moser, J.K.: Lectures in Celestial Mechanics, Springer-Verlag (1971)

    Google Scholar 

  7. Weinstein, A.: Simple Periodic Orbits in Topics in Nonlinear Dynamics, ed. S.Jorna, American Inst. Ph. Conf. Proc. 46 (1978).

    Google Scholar 

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© 1979 Springer-Verlag

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van der Aa, E., Sanders, J.A. (1979). The 1:2:1-resonance, its periodic orbits and integrals. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062954

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  • DOI: https://doi.org/10.1007/BFb0062954

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09245-2

  • Online ISBN: 978-3-540-35332-4

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