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Book Review
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Book Information
Author(s):
Alexander D. Bruno
Title:
Local methods in nonlinear differential equations
Additional book information:
(Translated by William Hovingh and Courtney S. Coleman), Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, Heidelberg, New York, 1989, x + 348 pp., $119.00. ISBN 0-387-18926-2
References:
- 1.
- V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, Berlin, 1983. MR 695786
- 2.
- R. I. Bogdanov, Versal deformations of a singular point on the plane in the case of zero eigenvalues, Functional Anal. Appl. 9 (2) (1975), 44-145. MR 380878
- 3.
- J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Applied Mathematical Sciences, vol. 42, Springer-Verlag, Berlin, 1983. MR 709768
- 4.
- E. L. Ince, Ordinary differential equations, Longmans, Green and Co., London, 1926. (Reissued by Dover Publications, 1956.) MR 10757
- 5.
- A. Kelley, The stable, center-stable, center, center-unstable and unstable manifolds, J. Differential Equations 3 (1967), 546-570. MR 221044
- 6.
- V. A. Pliss, A reduction principle in the theory of the stability of motion, Izv. Akad. Nauk. SSR Math. Ser. 28 (1964), 1297-1324. MR 190449
- 7.
- H. Poincaré, Les methodes nouvelles de la mecanique celeste I-III, Gauthier-Villars, Paris, 1899.
- 8.
- R. H. Rand and D. Armbruster, Perturbation methods, bifurcation theory and computer algebra, Applied Mathematical Sciences, vol. 65, Springer-Verlag, Berlin, 1987. MR 911274
- 9.
- F. Takens, Normal forms for certain singularities of vector fields, Ann. Inst. Fourier (Grenoble) 23 (1973), 163-195. MR 365620
- 10.
- F. Takens, Unfolding certain singularities of vectorfields: generalized Hopf bifurcations, J. Differential Equations 14 (1973), 476-493. MR 339264
- 11.
- F. Takens, Singularities of vector fields, Publ. Math. IHES 43 (1974), 47-100. MR 339292
Additional Information:
Reviewer(s):
Philip
Holmes
Review Information:
Journal:
Bull. Amer. Math. Soc.
22
(1990),
339-343.
DOI:
10.1090/S0273-0979-1990-15903-8
PII:
S 0273-0979(1990)15903-8
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