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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 deformation of a singular point of a vector field on the plane in the case of zero eigenvalues, Funkcional Anal. i Priložen. 9 (1975), no. 2, 63 (Russian). MR 0380878
  • 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, Dover Publications, New York, 1944. MR 0010757
  • 5. Al Kelley, The stable, center-stable, center, center-unstable, unstable manifolds, J. Differential Equations 3 (1967), 546–570. MR 0221044
  • 6. V. A. Pliss, A reduction principle in the theory of stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1297–1324 (Russian). MR 0190449
  • 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. Floris Takens, Normal forms for certain singularities of vectorfields, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 2, 163–195 (English, with French summary). Colloque International sur l’Analyse et la Topologie Différentielle (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1972). MR 0365620
  • 10. Floris Takens, Unfoldings of certain singularities of vectorfields: generalized Hopf bifurcations, J. Differential Equations 14 (1973), 476–493. MR 0339264
  • 11. Floris Takens, Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 47–100. MR 0339292

Review Information:

Reviewer: Philip Holmes
Journal: Bull. Amer. Math. Soc. 22 (1990), 339-343