Andreas Knauf - Böcker
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4 produkter
4 produkter
Del 13 - Lecture Notes in Physics Monographs
Classical Planar Scattering by Coulombic Potentials
Häftad, Engelska, 2014
538 kr
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Astronomy as well as molecular physics describe non-relativistic motion by an interaction of the same form: By Newton's respectively by Coulomb's potential. But whereas the fundamental laws of motion thus have a simple form, the n-body problem withstood (for n > 2) all attempts of an explicit solution. Indeed, the studies of Poincare at the end of the last century lead to the conclusion that such an explicit solution should be impossible. Poincare himselfopened a new epoch for rational mechanics by asking qual itative questions like the one about the stability of the solar system. To a largeextent, his work, which was critical for the formation of differential geometry and topology, was motivated by problems arising in the analysis of the n-body problem ([38], p. 183). As it turned out, even by confining oneselfto questions ofqualitativenature, the general n-body problem could not be solved. Rather, simplified models were treated, like planar motion or the restricted 3-body problem, where the motion of a test particle did not influence the other two bodies.
1 175 kr
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As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior.
553 kr
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Ausgehend von interessanten Beispielen aus der Physik bietet dieses Buch auch in der zweiten Auflage nicht nur eine gelungene Auswahl grundlegender Ergebnisse der klassischen Mechanik, sondern auch einen Einstieg in aktuelle Forschungsgebiete aus diesem Bereich. Hierbei reicht das Themenspektrum von dynamischen Systemen bis hin zur Störungstheorie und zeigt den großen Formenreichtum des Gebiets auf, vom gut berechenbaren (integrablen) bis zum chaotischen (mischenden) Verhalten. Höhepunkte des Buches sind die Darstellung der KAM-Theorie (Kolmogorov-Arnold-Moser-Theorie) und ein Beweis der asymptotischen Vollständigkeit in der klassischen Streutheorie.Mit einer klaren inhaltlichen Struktur und konzentrierten Anhängen ist die Darstellung in sich geschlossen und setzt lediglich Kenntnisse der Grundvorlesungen in Mathematik voraus.
384 kr
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This book includes lectures given at the DMV seminar "Classical Nonintegrability, Quantum Chaos", and the aim of it is to provide an introduction to the ideas and mathematical techniques of classical and quantum nonlinear dynamics. The section by Viviane Baladi gives an overview of the current literature and includes a discussion of the problems and results in that literature. The chapters on irregular scattering and expanding maps illustrate techniques in nonlinear dynamics using simple but nontrivial examples. The chapters on quantum chaos and on Liouville surfaces emphasize a phase space geometry approach to semi-classical quantum theory.