This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen 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 theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume. Contributors: Fred C. Adams Henk W. Broer Anthony M. Bloch Tomas Caraballo David R.J. Chillingworth Freddy Dumortier Messoud Efendiev Tor Flå Peter A. Giesl Christoph Glocker Alexandra Goeke John Guckenheimer Sigurdur Hafstein Heinz Hanßmann Darryl D. Holm Hany  A. Hosham Eric W. Justh Peter E. Kloeden P. S. Krishnaprasad Martin Kružík Tassilo Küpper Alexander Mielke James Montaldi Philip J. Morrison Jonathan Munn Arne B. Nordmark Marius Paicu Tudor S. Ratiu Geneviève Raugel Sebastian Reich Michael Renardy Florian H.-H. Rupp Björn Sandstede Samuel N. Stechmann Tadashi Tokieda André Vanderbauwhede Sebastian Walcher Daniel Weiss Clemens Woywod Jiangong You Fumin Zhang Anna Zhigun Johannes Zimmer.