Bulletin of the American Mathematical Society

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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.

J. C. Alexander and James A. Yorke, Global bifurcations of periodic orbits, Amer. J. Math. 100 (1978), no. 2, 263–292. MR 474406, DOI 10.2307/2373851

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.

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

Jorge Ize, Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc. 7 (1976), no. 174, viii+128. MR 425696, DOI 10.1090/memo/0174

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, 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

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 10.1007/BF02416564

David Ruelle and Floris Takens, On the nature of turbulence, Comm. Math. Phys. 20 (1971), 167–192. MR 284067

Floris Takens, Forced oscillations and bifurcations, Global analysis of dynamical systems, Inst. Phys., Bristol, 2001, pp. 1–61. MR 1858470

Floris Takens, Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 47–100. MR 339292

J. C. Alexander and J. Yorke (1978), Global bifurcations of periodic orbits, Amer. J. Math. 100, 263-292. MR 0474406




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.




P. J. Holmes, editor (1980), New approaches to nonlinear problems in dynamics, SIAM. 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




D. Rand (1982), Dynamics and symmetry. Predictions for modulated waves in rotating fluids, Arch. Rational Mech. Anal. 79, 1-37. MR 654913




D. Ruelle and F. Takens (1971), On the nature of turbulence, Comm. Math. Phys. 20, 167-192. MR 284067




F. Takens (1974a), Forced oscillations and bifurcations, Communication 3, Math. Inst., Rijksuniversiteit, Utrecht. MR 1858470




F. Takens (1974), Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43, 47-100. MR 339292