Nonlinear Differential Equations and Dynamical Systems.

Universitext -- Nonlinear Differential Equations and Dynamical Systems -- Copyright -- Preface -- Contents -- 1 Introduction -- 2 Autonomous equations -- 3 Critical points -- 4 Periodic solutions -- 5 Introduction to the theory of stability -- 6 Linear Equations -- 7 Stability by linearisation -- 8 Stability analysis by the direct method -- 9 Introduction to perturbation theory -- 10 The Poincaré-Lindstedt method -- 11 The method of averaging -- 12 Relaxation Oscillations -- 13 Bifurcation Theory -- 14 Chaos -- 15 Hamiltonian systems -- Appendix 1: The Morse lemma -- Appendix 2: Linear periodic equations with a small parameter -- Appendix 3: Trigonometric formulas and averages -- Appendix 4: A sketch of Cotton's proof of the stable and unstable manifold theorem 3.3 -- Appendix 5: Bifurcations of self-excited oscillations -- Appendix 6: Normal forms of Hamiltonian systems near equilibria -- Answers and hints to the exercises -- References -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.