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Hamiltonian Dynamical Systems and Applications (Paperback, 2008 ed.)
Loot Price: R5,491
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Hamiltonian Dynamical Systems and Applications (Paperback, 2008 ed.)
Series: NATO Science for Peace and Security Series B: Physics and Biophysics
Expected to ship within 10 - 15 working days
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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 problems can 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. Applications are also presented to several
important areas of research, including problems in classical
mechanics, continuum mechanics, and partial differential equations.
These lecture notes cover many areas of recent mathematical
progress in this field, including the new choreographies of many
body orbits, the development of rigorous averaging methods which
give hope for realistic long time stability results, the
development of KAM theory for partial differential equations in one
and in higher dimensions, and the new developments in the long
outstanding problem of Arnold diffusion. It also includes other
contributions to celestial mechanics, to control theory, to partial
differential equations of fluid dynamics, and to the theory of
adiabatic invariants. In particular the last several years hasseen
major progress on the problems of KAM theory and Arnold diffusion;
accordingly, this volume includes lectures on recent developments
of KAM theory in infinite dimensional phase space, and descriptions
of Arnold diffusion using variational methods as well as
geometrical approaches to the gap problem. The subjects in question
involve by necessity some of the most technical aspects of analysis
coming from a number of diverse fields. Before the present volume,
there has not been one text nor one course of study in which
advanced students or experienced researchers from other areas can
obtain an overview and background to enter this research area. This
volume offers this, in an unparalleled series of extended lectures
encompassing this wide spectrum of topics in PDE and dynamical
systems.
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