Böcker i Frontiers in Applied Dynamical Systems: Reviews and Tutorials-serien

This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids.  The text uses the particular example of taffy pulling devices to represent pseudo-Anosov maps in practice.  In addition, its final chapters also briefly discuss current applications in the emerging field of analyzing braids created from trajectory data.  While written with beginning graduate students, advanced undergraduates, or practicing applied mathematicians in mind, the book is also suitable for pure mathematicians seeking real-world examples.  Readers can benefit from some knowledge of homotopy and homology groups, but these concepts are briefly reviewed.  Some familiarity with Matlab is also helpful for the computational examples.

The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations.

Mathematics for a nonsmooth world.- 1930-2010: Nonsmooth dynamics'' linear age.- Discontinuities to model missing knowledge.- Three experiments.- Layers and implementations.- Ideal and non-ideal sliding.- The three experiments revisited.- Further curiosities of hidden dynamics.- Closing remarks: open challenges. 

Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT).It is the first of its kind that introduces the GSPT in a coordinate-independent manner.