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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Yuri A. Kuznetsov
Title: Elements of applied bifurcation theory
Additional book information: Applied Mathematical Sciences, vol. 112, Springer-Verlag, Berlin and New York, 1995, xv+515 pp., ISBN 0-387-94418-4, $59.95$

References [Enhancements On Off] (What's this?)

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  • A. Andronov and L. Pontryagin, Systémes grossieres, Dokl. Acad. Nauk SSSR 14 (1937), 247–251.
  • V. I. Arn$^\prime$old, V. Afraimovich, Y. Il$^\prime$yashenko, and L. Sil$^\prime$nikov, Theory of bifurcations, vol. 5, Encyclopaedia of Mathematical Sciences (V. I. Arn$^\prime$old, ed.), Springer-Verlag, Berlin and New York, 1994.
  • V. I. Arnol′d, Geometrical methods in the theory of ordinary differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250, Springer-Verlag, New York-Berlin, 1983. Translated from the Russian by Joseph Szücs; Translation edited by Mark Levi. MR 695786
  • D. K. Arrowsmith and C. M. Place, An introduction to dynamical systems, Cambridge University Press, Cambridge, 1990. MR 1069752
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  • G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., Providence, RI, 1927.
  • A. Chenciner, Courbes fermes invariantes non normalement hyperboliques au voisinage d’une bifurcation de Hopf dégénérée de diffeomorphismes de $\mathbb R^2$, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), 507–510.
  • Shui Nee Chow and Jack K. Hale, Methods of bifurcation theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 251, Springer-Verlag, New York-Berlin, 1982. MR 660633
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  • J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical systems & bifurcations of vector fields, Springer-Verlag, Berlin and New York, 1983.
  • J. E. Marsden and M. McCracken, The Hopf bifurcation and its applications, Applied Mathematical Sciences, Vol. 19, Springer-Verlag, New York, 1976. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt and S. Smale. MR 0494309
  • H. Poincaré, Mémoire sur les courbes definies par les équations differentielles I-IV, Oeuvre I, Gauthier-Villar, Paris, 1928.
  • L. P. Šil′nikov, A case of the existence of a denumerable set of periodic motions, Dokl. Akad. Nauk SSSR 160 (1965), 558–561 (Russian). MR 0173047
  • S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
  • Floris Takens, Forced oscillations and bifurcations, Applications of global analysis, I (Sympos., Utrecht State Univ., Utrecht, 1973) Comm. Math. Inst. Rijksuniv. Utrecht, No. 3-1974, Math. Inst. Rijksuniv. Utrecht, Utrecht, 1974, pp. 1–59. MR 0478235
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  • Review Information:

    Reviewer: David K. Arrowsmith
    Affiliation: Queen Mary & Westfield College University of London
    Journal: Bull. Amer. Math. Soc. 33 (1996), 377-380
    Review copyright: © Copyright 1996 American Mathematical Society