Introduction to the Perturbation Theory of Hamiltonian Systems

di Dmitry Treschev (Autore)

Oleg Zubelevich (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2012

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.

• Autore: Dmitry Treschev, Oleg Zubelevich
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Springer Monographs in Mathematics
• Anno: 2012
• Rilegatura: Paperback / softback
• Pagine: 211 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783642261046

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