Omohundro S.M. Geometric Perturbation Theory In Physics

World Scientific, 1986. — 588 p.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.Preface
Acknowledgement
Introduction
Mechanics
Survey of Geometric Perturbation Theory
Pseudo-forces and Reduction
Hamiltonian Structures in Perturbation Theory
Kruskal’s Theory of Nearly Periodic Systems
Ponderomotrve Force and Gyromotion
Waves
Asymptotic Wave Theory
A Hamiltonian Approach to Wave Modulation
A Lie Poisson Bracket for Wave Action Density
Dissipation and Statistics
Imbedding and Projection Theorems
Projected Area and Canonical Transformations
Reversibility vs. Irreversibility
Hamiltonian Dissipation in Infinite Dimensions
Reinsertion in Area-Preserving Horseshoes
Renormalisation Group
Symplectic Thermodynamics from Maximum Entropy
Glossary of Terms
Bibliography