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portada introduction to the perturbation theory of hamiltonian systems
Type
Physical Book
Publisher
Year
2012
Language
English
Pages
211
Format
Paperback
Dimensions
23.4 x 15.6 x 1.2 cm
Weight
0.32 kg.
ISBN
3642261043
ISBN13
9783642261046

introduction to the perturbation theory of hamiltonian systems

Dmitry Treschev (Author) · Oleg Zubelevich (Author) · Springer · Paperback

introduction to the perturbation theory of hamiltonian systems - Treschev, Dmitry ; Zubelevich, Oleg

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£ 115.52

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Synopsis "introduction to the perturbation theory of hamiltonian systems"

This book is an extended version of lectures given by the ?rst author in 1995-1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics, physics, chemistry, and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.

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