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This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.

Hamiltonian systems --- Systèmes hamiltoniens --- Congresses. --- Congrès --- Hamiltonian systems. --- Mathematics. --- Differentiable dynamical systems. --- Differential equations, partial. --- Cell aggregation --- Thermodynamics. --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Mechanics, Fluids, Thermodynamics. --- Mathematical Theory --- Geometry --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Aggregation, Cell --- Cell patterning --- Partial differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Math --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Manifolds (Mathematics). --- Complex manifolds. --- Classical and Continuum Physics. --- Science --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cell interaction --- Microbial aggregation --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Continuum physics. --- Classical field theory --- Continuum physics --- Continuum mechanics --- Differentiable dynamical systems

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Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally,Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.

Hydrodynamics --- Stochastic processes --- Hydrodynamique --- Processus stochastiques --- Congresses. --- Mathematical models --- Congresses --- Congrès --- Modèles mathématiques --- Applied Mathematics --- Calculus --- Mathematical Theory --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Probabilities. --- Physics. --- Continuum physics. --- Analysis. --- Probability Theory and Stochastic Processes. --- Classical Continuum Physics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- 517.1 Mathematical analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Partial differential equations --- Math --- Science --- Fluid dynamics --- Global analysis (Mathematics). --- Distribution (Probability theory. --- Differential equations, partial. --- Mathematical physics. --- Classical and Continuum Physics. --- Physical mathematics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Stochastic partial differential equations --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Differential equations, Partial