Bulletin of the American Mathematical Society

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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.

V. I. Arnol′d, Geometrical methods in the theory of ordinary differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250, Springer-Verlag, New York-Berlin, 1983. Translated from the Russian by Joseph Szücs; Translation edited by Mark Levi. MR 695786

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

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, DOI 10.1007/978-1-4612-1140-2

E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757

Al Kelley, The stable, center-stable, center, center-unstable, unstable manifolds, J. Differential Equations 3 (1967), 546–570. MR 221044, DOI 10.1016/0022-0396(67)90016-2

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.

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, DOI 10.1007/978-1-4612-1060-3

Floris Takens, Normal forms for certain singularities of vectorfields, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 2, 163–195 (English, with French summary). MR 365620

Floris Takens, Unfoldings of certain singularities of vectorfields: generalized Hopf bifurcations, J. Differential Equations 14 (1973), 476–493. MR 339264, DOI 10.1016/0022-0396(73)90062-4

Floris Takens, Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 47–100. MR 339292

1.

V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, Berlin, 1983. MR 0695786

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