Ordinary Differential Equations: Qualitative Theory (Graduate Studies in Mathematics, 137)

This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems. In a comprehensive introduction to the qualitative theory of ordinary differential equations, Barreira and Valls (both mathematics, Instituto Superior Técnico, Portugal) focus on the existence and uniqueness of solution, phase portraits, linear equations and their perturbations, stability and Lyapunov functions, hyperbolicity, and equations in the plane. The book can support a second course on ordinary differential equations, but has enough material to be used several different ways as well, such as advanced graduate courses on stability or hyperbolicity. The Portuguese edition, Equações diferenciais: Teoria Qualitativa, was published by IST Press in 2010, and was translated by the authors. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com) Chapter 1. Ordinary Differential Equations Chapter 2. Linear Equations And Conjugacies Chapter 3. Stability And Lyapunov Functions Chapter 4. Hyperbolicity And Topological Conjugacies Chapter 5. Existence Of Invariant Manifolds Chapter 6. Index Theory Chapter 7. Poincaré-bendixson Theory Chapter 8. Bifurcations And Center Manifolds Chapter 9. Hamiltonian Systems Luis Barreira, Claudia Valls ; Translated By The Authors. Includes Bibliographical References (p. 243-244) And Index.