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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

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:

Bibliography

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S. N. Chow and J. K. Hale, Methods of bifurcation theory, Springer-Verlag, New York, 1982. MR 660633 (84e:58019)

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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)

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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)

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-, Imperfect bifurcation in the presence of symmetry, Comm. Math. Phys. 67 (1979), 205-232. MR 539727 (80j:58017)

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J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical systems and bifurcation of vector fields, Springer-Verlag, New York, 1983. MR 709768 (85f:58002)

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[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]
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S. Smale, Structurally stable systems are not dense, Amer. J. Math. 86 (1966), 491-496. MR 0196725 (33:4911)

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-, 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)

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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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