Buch, Englisch, 211 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g
Buch, Englisch, 211 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g
Reihe: Springer Monographs in Mathematics
ISBN: 978-3-642-26104-6
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
Hamiltonian Equations.- to the KAM Theory.- Splitting of Asymptotic Manifolds.- The Separatrix Map.- Width of the Stochastic Layer.- The Continuous Averaging Method.- The Anti-Integrable Limit.- Hill’s Formula.
