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Bulletin of the American Mathematical Society

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Book Review

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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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  • G. Hermann (1967a), Stability of equilibrium of elastic systems subjected to nonconservative forces, Appl. Mech. Rev. 20, 103-108.
  • 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.
  • E. Hopf (1942), Abzweigung einer periodischer Lösung von einer stationaren Lösung eines Differentialsystems, Ber. Verh. Säch. Akad. Wiss. Leipzig Math.-Nat 94, 3-22; English transl. by L. N. Howard and N. Kopell in Marsden and McCracken (1976). MR 39141
  • J. Ize (1976), Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc. No. 174. MR 425696
  • D. D. Joseph (1976), Stability of fluid motions, vols. I, II, Springer-Verlag, Berlin and New York.
  • J. E. Marsden and M. McCracken (1976), The Hopf bifurcation and its applications, Springer-Verlag, Berlin and New York. MR 494309
  • David Rand, Dynamics and symmetry. Predictions for modulated waves in rotating fluids, Arch. Rational Mech. Anal. 79 (1982), no. 1, 1–37. MR 654913,
  • D. Ruelle and F. Takens (1971), On the nature of turbulence, Comm. Math. Phys. 20, 167-192. MR 284067
  • Floris Takens, Forced oscillations and bifurcations, Global analysis of dynamical systems, Inst. Phys., Bristol, 2001, pp. 1–61. MR 1858470
  • F. Takens (1974), Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43, 47-100. MR 339292

Review Information:

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