Nonlinear Differential Equations and Dynamical SystemsFeaturing five incredible women who will prove to be every bit as beloved as Lou Clark, the unforgettable heroine of Me Before You. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincare. The global direct method is then discussed. To obtain more quantitative information the Poincare-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems recurrence, invariant tori, periodic solutions. The book presents the subject material from both the qualitative and the quantitative point of view.
Ordinary Differential Equations, Spring 2002 (G63.2470)
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Koon, M. Lo, J. Marsden and S. Chapter 2 Chapter 6 Chapter 7 References on periodic orbits and their computation Divakar Viswanath  The Lindstedt-Poincare technique as an algorithm for computing periodic orbits. SIAM Review 43 3 , Worfolk  The geometry of halo orbits in the circular restricted three-body problem.
He graduated at the University of Amsterdam in Astrophysics and Mathematics. A period of five years at the Technological University of Delft, started his interest in technological problems, resulting in various cooperations with engineers. His other interests include the methods and applications of asymptotic analysis, nonlinear oscillations and wave theory. He holds a chair of dynamical systems at the department of mathematics at the University of Utrecht. Among his other interests are a publishing company, Epsilon Uitgaven, that he founded in , and the relation between dynamical systems and psychoanalysis.
It seems that you're in Germany. We have a dedicated site for Germany. On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension.