Book Review
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Book Information:
Author:
Yuri A. Kuznetsov
Title:
Elements of applied bifurcation theory
Additional book information:
Applied Mathematical Sciences, vol. 112, Springer-Verlag,
Berlin and New York,
1995,
xv+515 pp.,
ISBN 0-387-94418-4,
$59.95$
A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maĭer, Theory of bifurcations of dynamic systems on a plane, Halsted Press [John Wiley & Sons], New York-Toronto; Israel Program for Scientific Translations, Jerusalem-London, 1973. Translated from the Russian. MR 0344606
A. Andronov and L. Pontryagin, Systémes grossieres, Dokl. Acad. Nauk SSSR 14 (1937), 247–251.
V. I. Arn$^\prime$old, V. Afraimovich, Y. Il$^\prime$yashenko, and L. Sil$^\prime$nikov, Theory of bifurcations, vol. 5, Encyclopaedia of Mathematical Sciences (V. I. Arn$^\prime$old, ed.), Springer-Verlag, Berlin and New York, 1994.
V. I. Arnol′d, Geometrical methods in the theory of ordinary differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250, Springer-Verlag, New York-Berlin, 1983. Translated from the Russian by Joseph Szücs; Translation edited by Mark Levi. MR 695786
D. K. Arrowsmith and C. M. Place, An introduction to dynamical systems, Cambridge University Press, Cambridge, 1990. MR 1069752
R. Bogdanov, Bifurcations of a limit cycle for a family of vector fields on the plane, Selecta Math. Soviet 1 (4) (1981), 373–388.
G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., Providence, RI, 1927.
A. Chenciner, Courbes fermes invariantes non normalement hyperboliques au voisinage d’une bifurcation de Hopf dégénérée de diffeomorphismes de $\mathbb R^2$, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), 507–510.
Shui Nee Chow and Jack K. Hale, Methods of bifurcation theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 251, Springer-Verlag, New York-Berlin, 1982. MR 660633
F. Dumortier, R. Roussarie, J. Sotomayor, and H. Żołądek, Bifurcations of planar vector fields, Lecture Notes in Mathematics, vol. 1480, Springer-Verlag, Berlin, 1991. Nilpotent singularities and Abelian integrals. MR 1166189, DOI 10.1007/BFb0098353
J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical systems & bifurcations of vector fields, Springer-Verlag, Berlin and New York, 1983.
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
H. Poincaré, Mémoire sur les courbes definies par les équations differentielles I-IV, Oeuvre I, Gauthier-Villar, Paris, 1928.
L. P. Šil′nikov, A case of the existence of a denumerable set of periodic motions, Dokl. Akad. Nauk SSSR 160 (1965), 558–561 (Russian). MR 0173047
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
Floris Takens, Forced oscillations and bifurcations, Applications of global analysis, I (Sympos., Utrecht State Univ., Utrecht, 1973) Comm. Math. Inst. Rijksuniv. Utrecht, No. 3-1974, Math. Inst. Rijksuniv. Utrecht, Utrecht, 1974, pp. 1–59. MR 0478235
Stephen Wiggins, Global bifurcations and chaos, Applied Mathematical Sciences, vol. 73, Springer-Verlag, New York, 1988. Analytical methods. MR 956468, DOI 10.1007/978-1-4612-1042-9
- A. Andronov, E. Leontovich, I. Gordon, and A. Maier, Theory of bifurcations of dynamical systems on a plane, Israel Prog. for Sci. Trans., 1973.
- A. Andronov and L. Pontryagin, Systémes grossieres, Dokl. Acad. Nauk SSSR 14 (1937), 247–251.
- V. I. Arn$^\prime$old, V. Afraimovich, Y. Il$^\prime$yashenko, and L. Sil$^\prime$nikov, Theory of bifurcations, vol. 5, Encyclopaedia of Mathematical Sciences (V. I. Arn$^\prime$old, ed.), Springer-Verlag, Berlin and New York, 1994.
- V. I. Arn$^\prime$old, Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, Berlin and New York, 1983.
- D. K. Arrowsmith and C. M. Place, Introduction to dynamical systems, Cambridge Univ. Press, Cambridge, 1990.
- R. Bogdanov, Bifurcations of a limit cycle for a family of vector fields on the plane, Selecta Math. Soviet 1 (4) (1981), 373–388.
- G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., Providence, RI, 1927.
- A. Chenciner, Courbes fermes invariantes non normalement hyperboliques au voisinage d’une bifurcation de Hopf dégénérée de diffeomorphismes de $\mathbb R^2$, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), 507–510.
- S.-N. Chow and J. K. Hale, Methods of bifurcation theory, Springer-Verlag, Berlin and New York, 1982.
- F. Dumortier, R. Roussarie, J. Sotomayor, and H. Zoladek, Bifurcations of planar vector fields, Springer-Verlag, Berlin and New York, 1991.
- J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical systems & bifurcations of vector fields, Springer-Verlag, Berlin and New York, 1983.
- J. Marsden and M. McCracken, Hopf bifurcation and its applications, Springer-Verlag, Berlin and New York, 1976.
- H. Poincaré, Mémoire sur les courbes definies par les équations differentielles I-IV, Oeuvre I, Gauthier-Villar, Paris, 1928.
- L. Sil$^\prime$nikov, A case of a denumerable set of periodic motions, Dokl. Akad. Nauk SSSR 160 (1965), 558–561.
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817.
- F. Takens, Forced oscillations and bifurcations, Comm. Math. Inst., Rijksununiversiteit Utrecht 2 (1974), 1–111.
- S. Wiggins, Global bifurcations and chaos, Springer-Verlag, Berlin and New York, 1988.
Review Information:
Reviewer:
David K. Arrowsmith
Affiliation:
Queen Mary & Westfield College University of London
Email:
D.K.Arrowsmith@qmw.ac.uk
Journal:
Bull. Amer. Math. Soc.
33 (1996), 377-380
DOI:
https://doi.org/10.1090/S0273-0979-96-00665-9
Review copyright:
© Copyright 1996
American Mathematical Society
