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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Author: 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 [Enhancements On Off] (What's this?)

  • 1. V. I. Arnol′d, Geometrical methods in the theory of ordinary differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 250, Springer-Verlag, New York-Berlin, 1983. Translated from the Russian by Joseph Szücs; Translation edited by Mark Levi. 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. John Guckenheimer and Philip Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences, vol. 42, Springer-Verlag, New York, 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. Richard H. Rand and Dieter Armbruster, Perturbation methods, bifurcation theory and computer algebra, Applied Mathematical Sciences, vol. 65, Springer-Verlag, New York, 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

Review Information:

Reviewer: Philip Holmes
Journal: Bull. Amer. Math. Soc. 22 (1990), 339-343
DOI: https://doi.org/10.1090/S0273-0979-1990-15903-8
American Mathematical Society