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Ordinary Differential Equations: Qualitative Theory

About this Title

Luis Barreira, Instituto Superior Técnico, Lisbon, Portugal and Claudia Valls, Instituto Superior Técnico, Lisbon, Portugal. Translated by Luis Barreira, Instituto Superior Técnico, Lisbon, Portugal and Claudia Valls, Instituto Superior Técnico, Lisbon, Portugal

Publication: Graduate Studies in Mathematics
Publication Year: 2012; Volume 137
ISBNs: 978-0-8218-8749-3 (print); 978-0-8218-8993-0 (online)
DOI: https://doi.org/10.1090/gsm/137
MathSciNet review: MR2931599
MSC: Primary 34-01; Secondary 37Dxx, 37Gxx, 37Jxx

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Table of Contents

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Front/Back Matter

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Part 1. Basic concepts and linear equations

• Chapter 1. Ordinary differential equations
• Chapter 2. Linear equations and conjugacies

Part 2. Stability of hyperbolicity

• Chapter 3. Stability and Lyapunov functions
• Chapter 4. Hyperbolicity and topological conjugacies
• Chapter 5. Existence of invariant manifolds

Part 3. Equations in the plane

• Chapter 6. Index theory
• Chapter 7. Poincaré-Bendixson theory

Part 4. Further topics

• Chapter 8. Bifurcations and center manifolds
• Chapter 9. Hamiltonian systems