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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF

Book Information

Authors: J. E. Marsden and M. McCracken
Title: The Hopf bifurcation and its applications
Additional book information Springer-Verlag, New York, 1976, xiii + 408 pp., $14.80.


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

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  • 2. A. A. Andronov and A. A. Witt, Sur la théorie mathématiques des autooscillations, C. R. Acad. Sci. Paris 190 (1930), 256-258.
  • 3. Salomon Bochner and Deane Montgomery, Groups of differentiable and real or complex analytic transformations, Ann. of Math. (2) 46 (1945), 685–694. MR 0014102 (7,241d)
  • 4. Nathaniel Chafee, The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential system, J. Differential Equations 4 (1968), 661–679. MR 0229930 (37 #5496)
  • 5. Michael G. Crandall and Paul H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal. 52 (1973), 161–180. MR 0341212 (49 #5962)
  • 6. E. Conway, D. Hoff and J. Smoller, Large-time behavior of systems of nonlinear reaction-diffusion equations, S.I.A.M. J. Appl. Math. (to appear).
  • 7. B. D. Hassard, Bifurcation of periodic solutions of the Hodgkin-Huxley model for the current-clamped squid giant axon, J. Theoret. Biology (to appear).
  • 8. B. Hassard and Y. H. Wan, Bifurcation formulae derived from center manifold theory, J. Math. Anal. Appl. 63 (1978), no. 1, 297–312. MR 0488152 (58 #7719)
  • 9. 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 0039141 (12,501c)
  • 10. Gérard Iooss, Existence et stabilité de la solution périodique secondaire intervenant dans les problèmes d’evolution du type Navier-Stokes, Arch. Rational Mech. Anal. 47 (1972), 301–329 (French). MR 0346350 (49 #11075)
  • 11. D. D. Joseph and D. H. Sattinger, Bifurcating time periodic solutions and their stability, Arch. Rational Mech. Anal. 45 (1972), 79–109. MR 0387844 (52 #8682)
  • 12. V. I. Judovich, The birth of proper oscillations in a fluid, Prikl. Math. Meh. 35 (1971), 638-655.
  • 13. A. Lindstedt, Differentialgleichungen der Störungstheorie. (8), Mém. Sci. St. Pétersbourgh 31 (1883).
  • 14. E. N. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci. 20 (1963), 130-141.
  • 15. M. Poincaré, Les méthodes nouvelles de la mécanique céleste. Vols. I, II, Gauthier-Villars et Fils, Paris, 1892 and 1893; Dover Publications, Inc., New York, 1957. MR 19, 414.
  • 16. David Ruelle and Floris Takens, On the nature of turbulence, Comm. Math. Phys. 20 (1971), 167–192. MR 0284067 (44 #1297)
  • 17. David H. Sattinger, Topics in stability and bifurcation theory, Lecture Notes in Mathematics, Vol. 309, Springer-Verlag, Berlin-New York, 1973. MR 0463624 (57 #3569)
  • 18. G. G. Stokes, On the theory of oscillatory waves, Cambridge Trans. 8 (1847), 441-473 (Papers vol. I, 197-229).
  • 19. W. Velte, Über ein Stabilitätskriterium der Hydrodynamik, Arch. Rational Mech. Anal. 9 (1962), 9–20 (German). MR 0155501 (27 #5435)
  • 20. R. F. Williams, The structure of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 73–99. MR 556583 (82b:58055b)


Review Information

Reviewer: Nicholas D. Kazarinoff
Journal: Bull. Amer. Math. Soc. 83 (1977), 998-1004
DOI: http://dx.doi.org/10.1090/S0002-9904-1977-14352-8
PII: S 0002-9904(1977)14352-8



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