Multiple Time Scale Dynamics

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.

"It merges a wide variety of different mathematical techniques into a more unified framework. ... this is a very interesting introduction to multiscale dynamics which will be of much assistance to both students and researchers. The target audience of this book is senior undergraduates and graduate students as well as researchers interested in using the theory of multiple time scale dynamics in nonlinear science, either from a theoretical or a mathematical modeling perspective." (Tewfik Sari, Mathematical Reviews, May, 2016) "This interesting monograph is a self-contained, coherent overview of the backgrounds and progress of the dynamical systems with multiple time scales. ... The book contains excellent mathematics and is a well-written and unique source of information on the multiple time scale dynamics. I highly recommend it to all researchers and graduate students who would like to understand the geometric singular perturbation theory." (Robert Vrabel, zbMATH 1335.34001, 2016)

• ​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.