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Versal Deformation of Singularities and Its Applications to Strange Attractors

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Chaos and Statistical Methods

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 24))

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Abstract

The aim of this article is to present a systematic mathematical method for the study of global bifurcation diagrams of families of autonomous ordinary differential equations. We employ the normal form and versai family theory developed in USHIKI[22], which is an improved version of classical normal form theory for singularities of vector fields. The classical theory for normal forms is known and has been employed in many authors to study the bifurcation of vector fields. See POINCARE[16][17][18], BIRKHOFF[6], ARNOLD[2][3][4][5], TAKENS[21] and BROER[8] for the classical theory and its modern version. See ARNOLD[4][5], BOGDANOV[7], LANGFORD[13], LANGFORD-IOOSS[14], GUCKENHEIMER[9], HOLMES[10][11], and ARNEODO-COULLET-SPIEGEL-TRESSER[1] for some applications of the normal forms theory to bifurcation problems.

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Authors and Affiliations

  1. Institute of Mathematics, Yoshida College, Kyoto University, Kyoto, 606, Japan

    S. Ushiki

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  1. S. Ushiki
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Editor information

Editors and Affiliations

  1. Research Institute for Fundamental Physics, Yukawa Hall, Kyoto University, 606, Kyoto, Japan

    Yoshiki Kuramoto

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© 1984 Springer-Verlag Berlin Heidelberg

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Ushiki, S. (1984). Versal Deformation of Singularities and Its Applications to Strange Attractors. In: Kuramoto, Y. (eds) Chaos and Statistical Methods. Springer Series in Synergetics, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69559-9_18

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  • DOI: https://doi.org/10.1007/978-3-642-69559-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69561-2

  • Online ISBN: 978-3-642-69559-9

  • eBook Packages: Springer Book Archive

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