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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:
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- [1]
- V. I. Arnold, Lectures on bifurcations in versal families, Russian Math. Surveys 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. MR 0209095 (35:1)
- [3]
- S. N. Chow and J. K. Hale, Methods of bifurcation theory, Springer-Verlag, New York, 1982. MR 660633 (84e:58019)
- [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 29 (1987), 95-127. MR 923885 (90d:58111a)
- [5]
- M. Field, Symmetry breaking for compact Lie groups, preprint, 1993. MR 1317939 (96j:58121)
- [6]
- M. Golubitsky and D. Schaeffer, A theory for imperfect bifurcation via singularity theory, Comm. Pure Appl. Math. 32 (1979), 21-98. MR 508917 (80j:58061)
- [7]
- -, Imperfect bifurcation in the presence of symmetry, Comm. Math. Phys. 67 (1979), 205-232. MR 539727 (80j:58017)
- [8]
- J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical systems and bifurcation of vector fields, Springer-Verlag, New York, 1983. MR 709768 (85f:58002)
- [9]
- J. E. Marsden and J. Scheurle, The construction and smoothness of invariant manifolds by the deformation method, SIAM J. Math. Anal. 18 (1987), 1261-1274. MR 902331 (88m:58096)
- [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. 51 (1975), 243-255. MR 0374564 (51:10764)
- [12]
- M. M. Peixoto, Structural stability on two-manifolds, Topology 1 (1962), 101-120. MR 0142859 (26:426)
- [13]
- H. Poincaré, Sur les courbes définies par les équations differentielles, C. R. Acad. Sci. Paris Sér. I Math. 90 (1880), 673-675.
- [14]
- S. Smale, Structurally stable systems are not dense, Amer. J. Math. 86 (1966), 491-496. MR 0196725 (33:4911)
- [15]
- -, Stable manifolds for differential equations and diffeomorphisms, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 18 (1963), 97-116. MR 0165537 (29:2818b)
- [16]
- A. N. Sositaisvili, Bifurcations of a topological type of a vector field near a singular point, Trudy Sem. Petrovsk. 1 (1975), 279-308 (in Russian). MR 0478239 (57:17724)
- [17]
- F. Takens, Singularities of vector fields, Inst. Hautes Études Sci. Publ Math. 43 (1974), 47-100. MR 0339292 (49:4052)
- [18]
- R. Thom, Stabilité structurelle et morphogénèse, W. A. Benjamin, Reading, MA, 1972. MR 0488155 (58:7722a)
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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