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The book comprises the proceedings of a conference on Dynamical Systems. Leading experts in this field present overviews of the current state of the theory and its applications to mechanics and physics. In particular, the conference focusses on the following aspects of the theory of Dynamical Systems: 1) Stability and bifurcation; 2) Geometric mechanics and control theory; 3) Invariant manifolds, attractors and chaos; 4) Fluid mechanics and elasticity; 5) Perturbations and multiscale problems; 6) Hamiltonian dynamics, KAM-Theory.