This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Christian Kuehn is a Postdoctoral Researcher at Vienna University of Technology, Institute for Analysis and Scientific Computing in Vienna, Austria. He received his PhD in Applied Mathematics from Cornell University in 2010. His research areas include: applied mathematics, differential equations, dynamical systems, numerical mathematics, and stochastics.
Introduction.- General Fenichel Theory.- Geometric Singular Perturbation Theory.- Normal Forms.- Direct Asymptotic Methods.- Tracking Invariant Manifolds.- The Blow-Up Method.- Singularities and Canards.- Advanced Asymptotic Methods.- Numerical Methods.- Computing Manifolds.- Scaling and Delay.- Oscillations.- Chaos in Fast-Slow Systems.- Stochastic Systems.- Topological Methods.- Spatial Dynamics.- Infinite Dimensions.- Other Topics.- Applications.
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Softcover reprint of the original 1st ed. 2015