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Bulletin of the American Mathematical Society

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

Book Review

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MathSciNet review: 1567452
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: J. Carr
Title: Applications of centre manifold theory
Additional book information: Applied Mathematical Sciences, vol. 35, Springer-Verlag, New York, 1981, 142 pp., $14.00. ISBN 0-3879-0557-4.

Authors: B. D. Hassard, N. D. Kazarinoff and Y.-H. Wan
Title: Theory and applications of Hopf bifurcation
Additional book information: London Mathematical Society Lecture Notes Series, No. 41, Cambridge Univ. Press, Cambridge, England, 1981, vi + 311 pp., $35.00. ISBN 0-5212-3158-2.

Authors: Gerard Iooss and Daniel D. Joseph
Title: Elementary stability and bifurcation theory
Additional book information: Springer-Verlag, New York, 1980, xv + 286 pp., $22.00. ISBN 0-3879-0526-X.

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

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    P. J. Holmes (1977), Bifurcation to divergence and flutter in flow induced oscillations―a finite dimensional analysis, J. Sound Vibration 53, 471-503.
  • Philip J. Holmes (ed.), New approaches to nonlinear problems in dynamics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1980. MR 584582
  • P. J. Holmes and J. E. Marsden (1978), Bifurcations to divergence and flutter in flow induced oscillations―an infinite dimensional analysis. Automatica 14, 367-384.
  • Eberhard Hopf, Abzweigung einer periodischen Lösung von einer stationären eines Differentialsystems, Ber. Verh. Sächs. Akad. Wiss. Leipzig Math.-Nat. Kl. 95 (1943), no. 1, 3–22 (German). MR 39141
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  • D. D. Joseph (1976), Stability of fluid motions, vols. I, II, Springer-Verlag, Berlin and New York.
  • J. E. Marsden and M. McCracken, The Hopf bifurcation and its applications, 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; Applied Mathematical Sciences, Vol. 19. MR 0494309
  • David Rand, Dynamics and symmetry. Predictions for modulated waves in rotating fluids, Arch. Rational Mech. Anal. 79 (1982), no. 1, 1–37. MR 654913, DOI
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  • Floris Takens, Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 47–100. MR 339292

Review Information:

Reviewer: Stuart S. Antman
Journal: Bull. Amer. Math. Soc. 9 (1983), 241-248