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Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions

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Elementary Stability and Bifurcation Theory

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

In Chapter IX we determined the conditions under which subharmonic solutions, nT-periodic solutions with integers n > 1, could bifurcate from forced T-periodic solutions.

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References

  • V. I. Arnold, Loss of stability of self-oscillations close to resonance and versai deformations of equivariant vector fields, Funk. Anal. Ego. Prilog. 11, 1–10 (1977).

    Article  Google Scholar 

  • J. Neimark, On some cases of periodic motions depending on parameters, Dokl. Akad. Nauk. SSR, 736–739 (1959).

    Google Scholar 

  • H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris 1892 (see §§37, 38).

    Google Scholar 

  • D. Ruelle and F. Takens, On the nature of turbulence, Com. Math. Phys. 20, 167–192 (1971).

    Google Scholar 

  • R. J. Sacker, On Invariant Surfaces and Bifurcation of Periodic Solutions of Ordinary Differential Equations, New York Univ. IMM-NYU 333 (1964).

    Google Scholar 

  • Y. H. Wan, Bifurcation into invariant tori at points of resonance, Arch. Rational Mech. Anal. 68, 343–357 (1978).

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Author information

Authors and Affiliations

  1. Faculté des Sciences, Institut des Mathématiques et Sciences Physiques, Université des Nice, 06034, Parc Valrose, Nice, France

    Gérard Iooss

  2. Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, USA

    Daniel D. Joseph

Authors
  1. Gérard Iooss
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  2. Daniel D. Joseph
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© 1980 Springer-Verlag New York Inc.

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Iooss, G., Joseph, D.D. (1980). Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions. In: Elementary Stability and Bifurcation Theory. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9336-8_11

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  • DOI: https://doi.org/10.1007/978-1-4684-9336-8_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-9338-2

  • Online ISBN: 978-1-4684-9336-8

  • eBook Packages: Springer Book Archive

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