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Book Review
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Book Information
Author(s):
Milan Medved, translated from Slovak by J. Hajnovicova and D. Halasova
Title:
Fundamentals of dynamical systems and bifurcation theory
Additional book information:
Adam Hilger, Bristol, Philadelphia, and New York, 1992, viii\,+\,293 pp., US$66.00. ISBN 0-7503-0150-3
References:
- [1]
- V. I. Arnold, Lectures on bifurcations in versal families, Russian Math. Surveys \textbf{27} (1972), 54--123.
- [2]
- G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., Providence, RI, 1927; rev. ed., 1966.
- [3]
- S. N. Chow and J. K. Hale, Methods of bifurcation theory, Springer-Verlag, New York, 1982.
- [4]
- C. Elphick, E. Tirapegui, M. Brachet, P. Coullet, and G. Iooss, A simple global characterization for normal forms of singular vector fields, Phys. D \textbf{29} (1987), 95--127.
- [5]
- M. Field, Symmetry breaking for compact Lie groups, preprint, 1993.
- [6]
- M. Golubitsky and D. Schaeffer, A theory for imperfect bifurcation via singularity theory, Comm. Pure Appl. Math. \textbf{32} (1979), 21--98.
- [7]
- M. Golubitsky and D. Schaeffer, Imperfect bifurcation in the presence of symmetry, Comm. Math. Phys. \textbf{67} (1979), 205--232.
- [8]
- J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical systems and bifurcation of vector fields, Springer-Verlag, New York, 1983.
- [9]
- J. E. Marsden and J. Scheurle, The construction and smoothness of invariant manifolds by the deformation method, SIAM J. Math. Anal. \textbf{18} (1987), 1261--1274.
- [10]
- J. Menck, Analysis of non-hyperbolic equilibria in dynamical systems by use of symmetries and computer algebra, Ph.D. Thesis, Univ. of Hamburg, 1992 (in German).
- [11]
- K. J. Palmer, Linearization near an integral manifold, J. Math. Anal. Appl. \textbf{51} (1975), 243--255.
- [12]
- M. M. Peixoto, Structural stability on two-manifolds, Topology \textbf{1} (1962), 101--120.
- [13]
- H. Poincar\'e, Sur les courbes d\'efinies par les \'equations differentielles, C. R. Acad. Sci. Paris S\'er. I Math. \textbf{90} (1880), 673--675.
- [14]
- S. Smale, Structurally stable systems are not dense, Amer. J. Math. \textbf{86} (1966), 491--496.
- [15]
- S. Smale, Stable manifolds for differential equations and diffeomorphisms, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) \textbf{18} (1963), 97--116.
- [16]
- A. N. Sositaisvili, Bifurcations of a topological type of a vector field near a singular point, Trudy Sem. Petrovsk. \textbf{1} (1975), 279--308 (in Russian).
- [17]
- F. Takens, Singularities of vector fields, Inst. Hautes \'Etudes Sci. Publ Math. \textbf{43} (1974), 47--100.
- [18]
- R. Thom, Stabilit\'e structurelle et morphog\'en\`ese, W. A. Benjamin, Reading, MA, 1972.
Additional Information:
Reviewer(s):
J\"urgen
Scheurle
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
142-146.
DOI:
10.1090/S0273-0979-1994-00501-4
PII:
S 0273-0979(1994)00501-4
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