Geometric Perturbation Theory in Physics

Geometric Perturbation Theory in Physics
2 089,- 2 089,-
Format E-Bok
Filformat PDF
Utgivelsesår 1986
Forlag World Scientific Publishing Co
Språk Engelsk
ISBN 9789814503150
Sider 584
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Om Geometric Perturbation Theory in Physics

This book which focusses on mechanics, waves and statistics, describes recent developments in the application of differential geometry, particularly symplectic geometry, to the foundations of broad areas of physics. Throughout the book, intuitive descriptions and diagrams are used to elucidate the mathematical theory. It develops a coordinate-free framework for perturbation theory and uses this to show how underlying symplectic structures arise from physical asymptotes. It describes a remarkable parity between classical mechanics which arises asymptotically from quantum mechanics and classical thermodynamics which arises asymptotically from statistical mechanics. Included here is a section with one hundred unanswered questions for further research. Contents:IntroductionSurvey of Geometric Perturbation Theory. Pseudo-Forces and ReductionHamiltonian Structures in Perturbation TheoryKruskal's Theory of Nearly Periodic SystemsPonderomotive Force and GyromotionAsymptotic Wave TheoryA Hamiltonian Approach to Wave ModulationA Lie-Poisson Bracket for Wave Action DensityImbedding and Projection TheoremsProjected Area and Canonical TransformationsReversibility vs. IrreversibilityHamiltonian Dissipation in Infinite DimensionsReinsertion in Area- Preserving HorseshoesRenormalization GroupSymplectic Thermodynamics from Maximum EntropyReadership: Mathematicians, physicists and applied mathematicians.Key Features:


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