Differential equations and dynamical systems. 2nd ed. (English) Zbl 0854.34001

Texts in Applied Mathematics. 7. New York, NY: Springer. xiv, 519 p. (1996).
The first edition (1991) has been reviewed in Zbl 0717.34001. From the preface to the second edition: “Several new sections have been added in the second edition of this book. Sections 2.12 and 2.13 on center manifold theory and normal forms which generalize the material in Section 2.11 for planar systems, are new. A more detailed development of Melnikov’s method, including some new theorems and their proofs and a new section on higher-order Melnikov theory, is given in Chapter 4. A discussion of the codimension and the universal unfolding of a bifurcation as well as some examples of higher codimension bifurcation, such as the Takens-Bogdanov bifurcation, have also been added in Chapter 4. The book ends with a new section on one of the author’s favorite research topics, a study of the bifurcations that occur in the class of bounded quadratic systems. The student is encouraged to participate in this research project by determining the bifurcation surfaces that occur in the class of bounded quadratic systems in the problem set at the end of Chapter 4”.


34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C23 Bifurcation theory for ordinary differential equations
34C30 Manifolds of solutions of ODE (MSC2000)


Zbl 0717.34001