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Some Properties of Second Order Dynamic Systems with Parametric Resonances

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Numerical Methods in the Study of Critical Phenomena

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 9))

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Abstract

The 1/2-subharmonic resonances of three particular dynamic systems are examined from the point of view of the theory of recurrences. It is found that the construction of approximate subharmonic solutions depends critically on the determination of characteristic exponents near bifurcations.

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References

  1. I. Gumowski, C. Mira: Dynamique Chaotique (Cépadues Editions, Toulouse 1980)

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  2. I. Gumowski, R. Thibault: Dynamic Systems with a Singular Parametric Resonance (Equadif-78, Firenze 1978) pp.91–98

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  5. R. Thibault: “Dynamic systems: Study of a Degenerate Subharmonic Bifurcation in a 2nd-Order Equation by the Separation of Solutions into Periodic and Antiperiodic Parts”, Proc. 8th ICNO, Prague (1978) pp.695–700

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Author information

Authors and Affiliations

  1. U.E.R. Mathématiques, Informatique et Gestion, Université Paul Sabatier, 118, Route de Narbonne, F-31062, Toulouse Cédex, France

    I. Gumowski

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  1. I. Gumowski
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Editors and Affiliations

  1. Laboratoire d’Informatique et de Mathématiques Appliquées de Grenoble, Université Scientifique et Médicale de Grenoble, F-BP 53X, 38041, Grenoble Cédex, France

    Jean Della Dora , Jacques Demongeot  & Bernard Lacolle ,  & 

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© 1981 Springer-Verlag Berlin Heidelberg

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Gumowski, I. (1981). Some Properties of Second Order Dynamic Systems with Parametric Resonances. In: Della Dora, J., Demongeot, J., Lacolle, B. (eds) Numerical Methods in the Study of Critical Phenomena. Springer Series in Synergetics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81703-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-81703-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81705-2

  • Online ISBN: 978-3-642-81703-8

  • eBook Packages: Springer Book Archive

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