Hamiltonian dynamical systems and applications: Proceedings of the NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications, Montréal, Canada, 18-29 June 2007

Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problemscan generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Lecture notes on current state ofthe art by the researchers who have developed the theory Introductions of thetechnically deep methods of Hamiltonian mechanics to partial differential equations Contains lectures on the most recent advances in KAM theory for partialdifferential equations INDICE: From the contents Preface.- Hamiltonian Dynamical Systems and Applications.- Some Aspects of Finite-Dimensional Hamiltonian Dynamics.- Four Lectures on the N-body Problem.- Average Method and Adiabatic Invariants.- Transformation Theory of Hamiltonian PDE and the Problem of Water Waves.- Three Theorems on Perturbed KdV.- Groups and Topology in the Euler Hydrodynamics and KdV.- Infinite Dimensional Dynamical Systems and the Navier-Stokes Equation.- Hamiltonian Systems and Optimal Control.- KAM Theory with Applications to Hamiltonian Partial Differential Equations.- Four Lectures on KAM for the Non-Linear Schrödinger Equation.- A Birkhoff Normal Form Theorem for some Semilinear PDEs.- Normal Forms for Holomorphic Dynamical Systems.- Geometric Approaches to theProblem of Instability in Hamiltonian Systems. An Informal Presentation.

• ISBN: 978-1-4020-6962-8
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 441
• Fecha Publicación: 01/02/2008
• Nº Volúmenes: 1
• Idioma: Inglés