A continuation approach to computing phase resetting curves -- Input-output networks, singularity theory, and homeostasis -- The approximation of invariant sets in infinite dimensional dynamical systems -- Set-oriented and finite-element study of coherent behavior in Rayleigh-Benard convection -- Singular value decomposition of operators on Reproducing Kernel Hilbert Spaces -- A weak characterization of slow variables in stochastic dynamical systems -- Analysis and simulation of extremes and rare events in complex systems -- Dynamical systems theory and algorithms for NP-hard problems.

This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.