This book presents the proceedings of a conference on dynamical systems held in honor of Jurgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation- Geometric mechanics and control theory- Invariant manifolds, attractors and chaos- Fluid mechanics and elasticity- Perturbations and multiscale problems- Hamiltonian dynamics and KAM theoryResearchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.