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Bifurcation: Analysis, Algorithms, Applications pp 71–82Cite as

Codimension Two Bifurcations Near an Invariant n-Torus

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Abstract

We consider a m-parameter C∞ -family of ordinary differential equations possessing an invariant n-dimensional torus.

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References

  1. Bibikov, Y. N. (1979) Local theory of nonlinear analytic ordinary differential equations, Leet. Notes Math. 702(Springer, Berlin).

    Google Scholar 

  2. Chow, S. N.&Hale, J. K. (1982) Methods in bifurcation theory, Grundlehren math. Wiss. 251(Springer, New York).

    Book  Google Scholar 

  3. Flockerzi, D. (1984) Generalized bifurcation of higher dimensional tori, JDE 55. 3, 346–367.

    Article  Google Scholar 

  4. Flockerzi, D. (1985) On the Tk→Tk+1 bifurcation problem, “Singularities&Dynamical Systems”, S. N. Pnevmatikos (ed.), North Holland, 35–46.

    Google Scholar 

  5. Flockerzi, D. (1986) Invariant manifolds and bifurcation of tori, Habilitationsschrift, Univ. Würzburg.

    Google Scholar 

  6. Flockerzi, D. (1986) Persistence and bifurcation of invariant tori, preprint 147, Univ. Würzburg.

    Google Scholar 

  7. Guckenheimer, J.&Holmes, P. (1983) Nonlinear oscillations dynamical systems and bifurcations of vector fields, Appl. Math. Sci. 42 (Springer, New York).

    Google Scholar 

  8. Guckenheimer, J. (1984) Multiple bifurcation problems of codimension two, SIAM J. math. Anal. 15. 1, 1–49.

    Article  Google Scholar 

  9. Iooss, G.&Langford, W. F. (1980) Conjectures on the routes to turbulence via bifurcations, “Nonlinear Dynamics”, R. H. G. Helleman(ed.), Annals of the NYAS Vol. 357, 489–505.

    Google Scholar 

  10. Langford, W. F. (1979) Periodic and steady-state interactions lead to tori, SIAM J. appl. Math. 37. 1, 22–48.

    Article  Google Scholar 

  11. Sacker, R. J.&Sell, G. R. (1978) Spectral theory for linear differential systems, JDE 27, 320–358.

    Google Scholar 

  12. Scheurle, J.&Marsden, J. (1984) Bifurcation to quasi-periodic tori in the interaction of steady state and Hopf bifurcations, SIAM J. math. Anal. 15. 6, 1055–1074.

    Article  Google Scholar 

  13. Sell, G, R. (1979) Bifurcation of higher dimensional tori, Arch. Rat. Mech. Anal. 69. 3, 199–230.

    Article  Google Scholar 

  14. Spirig, F. (1983) Sequence of bifurcations in a three-dimensional system near a critical point, ZAMP Vol. 34, 259–276.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Würzburg, Am Hubland, D-8700, Würzburg, West Germany

    Dietrich Flockerzi

Authors
  1. Dietrich Flockerzi
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Editor information

Editors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, D-3000, Hannover 1, Germany

    T. Küpper

  2. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, D-8700, Würzburg, Germany

    R. Seydel

  3. Institut für Mechanik, Technische Universität Wien, Karlsplatz 13, A-1040, Wien, Austria

    H. Troger

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© 1987 Birkhäuser Verlag Basel

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Flockerzi, D. (1987). Codimension Two Bifurcations Near an Invariant n-Torus. In: Küpper, T., Seydel, R., Troger, H. (eds) Bifurcation: Analysis, Algorithms, Applications. ISNM 79: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 79. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7241-6_8

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  • DOI: https://doi.org/10.1007/978-3-0348-7241-6_8

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7243-0

  • Online ISBN: 978-3-0348-7241-6

  • eBook Packages: Springer Book Archive

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