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Differential equations, dynamical systems, and an introduction to chaos. 2nd ed. (English) Zbl 1135.37002
Pure and Applied Mathematics (Amsterdam) 60. Amsterdam: Elsevier/Academic Press (ISBN 0-12-349703-5). xiv, 417 p. (2004).
This is an excellent text for an advanced undergraduate course in Differential Equations. It is a completely revised and updated version of the classic Hirsch-Smale text called “Differential Equations, Dynamical Systems and Linear Algebra” (see Zbl 0309.34001). According to the change in title, the linear algebra approach is less ambitious than in the first edition.
Contents: Preface; First Order Equations; Planar Linear Systems; Phase Portraits for Planar Systems; Classification of Planar Systems; Higher Dimensional Linear Algebra; Higher Dimensional Linear Systems; Nonlinear Systems; Equilibria in Nonlinear Systems; Global Nonlinear Techniques; Closed Orbits and Limit Sets; Applications in Biology; Applications in Circuit Theory; Applications in Mechanics; The Lorenz System; Discrete Dynamical Systems; Homoclinic Phenomena; Existence and Uniqueness Revisited.

MSC:
37-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory
34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
34Cxx Qualitative theory for ordinary differential equations
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