This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences.Contents: Volume 1: Celestial MechanicsHomoclinic TangenciesSingular PerturbationsStochastic SystemsSymmetryTopological Methods and Conley IndexDelay EquationsGeometric DynamicsHyperbolic Conservation LawsHyperbolic Wave EquationsHysteresisLarge DomainsLattice Dynamical SystemsMicrostructureNonlinear Functional AnalysisVariational MethodsViscosity SolutionsGlobal Attractors and LimitsNonautonomous AttractorsOrder-Preserving Dynamical SystemsQualitative Theory of Parabolic EquationsStability of Fronts and Pulses Volume 2: Computer Algebra ToolsControl and OptimizationDynamics and AlgorithmsExponentially Small PhenomenaGeometric IntegratorsNumerical Ergodic TheoryNumerics of DynamicsChemistryChemotaxis, Cross-Diffusion, and Blow-UpIndustrial ApplicationsMechanicsModels in Biology, Medicine, and PhysiologyMolecular ModellingPatternsSemiconductorsSteady Water WavesUnsteady Hydrodynamic WavesDelay EquationsNumericsOrdinary Differential EquationsPartial Differential Equations Key Features:The book completely differs from competing titles in that it gives a review of the microscopic methods, biophysical models and the experimental results obtained thereafter by the authors for a wide range of microscopic objects using the novel elaborated technique of digital holographic microscopyNovel data on the shape of human erythrocytes are presented