Front Cover; Dynamical Systems and Microphysics: Geometry and Mechanics; Copyright Page; Table of Contents; Contributors; Preface; PART I: GEOMETRIC STRUCTURES, MECHANICS, AND GENERAL RELATIVITY; CHAPTER 1. LAGRANGIAN SUBMANIFOLDS, STATICS AND DYNAMICS OF MECHANICAL SYSTEMS; 1. Lagrangian submanifolds of cotangent bundles; 2. Hamiltonian systems; CHAPTER 2. DEFORMATIONS AND QUANTIZATION; 1 -- CLASSICAL DYNAMICS AND SYMPLECTIC GEOMETRY; 2 -- HOCHSCHILD COHOMOLOGY AND CHEVALLEY COHOMOLOGY; 3 -- FORMAL DEFORMATIONS; 4 -- THE STAR PRODUCTS; 5 -- SYMPLECTIC CONNECTIONS AND THE SYMPLECTIC INVARIANT ß

6 -- THE VEY STAR-PRODUCTS7 -- INTRODUCTION TO A SPECTRAL THEORY AND QUANTIZATION; 8 -- THE CASE WHERE b2(W) = 0; 9 -- LIE ALGEBRAS GENERATED BY A WEAK TWISTED PRODUCT AND VEY LIE ALGEBRAS; 10 -- EXISTENCE THEOREM; 11 -- INVARIANT STAR PRODUCTS; CHAPTER 3. LIE GROUP ACTIONS ON POISSON AND CANONICAL MANIFOLDS; 1. POISSON MANIFOLDS; 2. CANONICAL MANIFOLDS; 3. AUTOMORPHISMS AND INFINITESIMAL AUTOMORPHISMS; 4. LIE GROUP ACTIONS; CHAPTER 4. GAUGE THEORIES AND GRAVITATION; 1. ANALYSIS OF MANIFOLDS; 2. HAMILTONIAN SYSTEMS; 3. MAXWELL'S EQUATIONS; 4. YANG-MILLS THEORIES; 5. GRAVITATION

CHAPTER 5. RIEMANNIAN GEOMETRY AND MECHANICS : THE KEPLER PROBLEM1. THE JACOBI SYSTEM.; 2. THE KEPLER PROBLEM; 3. CURVATURE AND MOTION; 4. GEODESIC FLOW AND PHASE SPACE; 5. THE SYMMETRY GROUP; 6. THE CASE n = 3; 7. THE COADJOINT REPRESENTATION; 8. ORBIT MANIFOLDS; 9. STABILITY OF PERIODIC ORBITS; CHAPTER 6. CONFINEMENT PROBLEMS IN MATHEMATICAL PHYSICS, CLASSICAL AND MODERN; 1. INTRODUCTION; 2. THE CLASSICAL EXAMPLES; 3. VORTICES IN TYPE II SUPERCONDUCTIVITY; 4. ADLER'S APPROACH TO QUARK CONFINEMENT; PART II: SYSTEM THEORY APPROACHES TO MECHANICS

CHAPTER 7. OPTIMALITY AND REACHABILITY WITH FEEDBACK CONTROL1. DYNAMICAL SYSTEM; 2. FEEDBACK CONTROL; 3. PLAYABILITY; 4. PERFORMANCE INDEX; 5. OPTIMALITY; 6. NECESSARY CONDITIONS -- A FUNCTIONAL EQUATION; 7. NECESSARY CONDITIONS -- AMINIMUM PRINCIPLE; 8. NECESSARY CONDITIONS -- TRANSVERSALITY; 9. SUMMARY OF NECESSARY CONDITIONS; 10. REACHABILITY; 11. EXAMPLE: TIME-OPTIMAL NAVIGATION; CHAPTER 8. OPTIMIZATION RELATIVISTIC AND CONTROLLABILITY IN PROBLEMS OF DYNAMICS AND OF GEOMETRICAL OPTICS; INTRODUCTION.; PART I : AN OPTIMAL CONTROL PROBLEM IN RELATIVISTIC DYNAMICS OF A MASS-POINT

1. PROBLEM STATEMENT, AND FIRST ASSUMPTIONS2. A FIRST BASIC PROPOSITION; 3. PATHS IN AUGMENTED STATE SPACE; 4. PROPOSITIONS 2 AND 3; 5. EXAMPLE 1; 6. EXAMPLE 2; 7. MECHANICAL INDEX OF REFRACTION; 8. THE PRINCIPLE OF PARALLEL TRANSPORT; 9. A CONNECTION WITH WAVE MECHANICS; PART II: A CONTROLLABILITY PROBLEM IN RELATIVISTIC DYNAMICS OF A MASS-POINT; 10. BASIC PROPOSITIONS; 11. EXAMPLE 1; 12. EXAMPLE 2; 13. A FAMILY OF SEMI-PERMEABLE SURFACES; 14. TRAJECTORIES IN SEMI-PERMEABLE SURFACES; 15. OPTICAL INDEX OF REFRACTION; 16. EQUATION OF EIKONALE