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Book Review
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Book Information
Author(s):
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
Author(s):
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
Author(s):
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:
- J. C. Alexander and J. Yorke (1978), Global bifurcations of periodic orbits, Amer. J. Math. 100, 263-292. MR 474406
- 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
Additional Information:
Reviewer(s):
Stuart S.
Antman
Review Information:
Journal:
Bull. Amer. Math. Soc.
9
(1983),
241-248.
DOI:
10.1090/S0273-0979-1983-15170-4
PII:
S 0273-0979(1983)15170-4
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