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Mathematical Physics: Classical Mechanics - Andreas Knauf

Mathematical Physics: Classical Mechanics

(Autor)

Buch | Softcover
XIV, 683 Seiten
2018 | 1st ed. 2018
Springer Berlin (Verlag)
978-3-662-55772-3 (ISBN)
CHF 149,75 inkl. MwSt

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics.

The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

Andreas Knauf is a professor of mathematics at the Friedrich-Alexander Universität Erlangen-Nürnberg. His research interests include classical, quantum and statistical mechanics. He is the author, with Markus Klein, of the book 'Classical Planar Scattering by Coulombic Potentials' and, with Yakov Sinai, of the book 'Classical Nonintegrability, Quantum Chaos'.

Remarks on Mathematial Physics.- 1 Introduction.- 2 Dynamical Systems.- 3 Ordinary Differential Equations.- 4 Linear Dynamics.- 5 Classification of Linear Flows.- 6 Hamiltonian Equations and Symplectic Group.- 7 Stability Theory.- 8 Variational Principles.- 9 Ergodic Theory.- 10 Symplectic Geometry.- 11 Motion in a Potential.- 12 Scattering Theory.- 13 Integrable Systems and Symmetries.- 14 Rigid and Non-Rigid Bodies.- 15 Perturbation Theory.- 16 Relativistic Mechanics.- 17 Symplectic Topology.- A Topological Spaces and Manifolds.- B Differential Forms.- C Convexity and Legendre Transform.- D Fixed Point Theorems, and Results about Inverse Images.- E Group Theory.- F Bundles, Connection, Curvature.- G Morse Theory.- H Solutions of the Exercises.- Bibiography.- Index of Proper Names.- Table of Symbols.- Image Credits.- Index.

Erscheinungsdatum
Reihe/Serie La Matematica per il 3+2
UNITEXT
Übersetzer Jochen Denzler
Zusatzinfo XIV, 683 p. 92 illus., 53 illus. in color.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 1041 g
Themenwelt Mathematik / Informatik Mathematik
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte classical mechanics • Dynamical Systems • ergodic theory • Hamiltonian Dynamics • Mathematical Physics • Mathematics • mathematics and statistics • Special Relativity Theory • Symplectic Geometry • Theoretical, Mathematical and Computational Physic
ISBN-10 3-662-55772-X / 366255772X
ISBN-13 978-3-662-55772-3 / 9783662557723
Zustand Neuware
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