This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view. A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects. The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others.

Computational Aspects of Differential Equations and Applications Water Waves Topological and Variational Methods Qualitative Theory of Nonlinear Parabolic and Elliptic Equations Around Hilbert's 16th Problem Navier stokes Equations and Reaction Diffusion Equations Hyperbolic Dynamics and Beyond Symmetry and Mechanics Shock Waves and Conservation Laws Nonlinear Elliptic Partial Differential Equations Algebraic Aspects and Optimisation in Dynamical Systems Case Studies in Theoretical Interpretation of Numerical Experiments Infinite-Dimensional Dynamics Quasiperiodicity Delay Equations Wave Stability and Pattern Formation Nonautonomous Dynamics Normal Forms and Invariant Manifolds Singular Perturbations Differential Geometric Foliations and Flows Homoclinic and Heteroclinic Dynamics Mathematical Aspects of Celestical Mechanics

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