Dynamical systems and microphysics : geometry and mechanics : the proceedings of the 2nd International Seminar on Mathematical Theory of Dynamical Systems and Microphysics held at the International Center for Mechanical Sciences at Udine, Italy, from September 1 to 11, 1981 /

Dynamical Systems and Microphysics.

Bibliographic Details
Call Number:Libro Electrónico
Corporate Author: International Seminar on Mathematical Theory of Dynamical Systems and Microphysics Udine, Italy
Other Authors: Avez, A. (Andr�e), Blaqui�ere, Austin, Marzollo, Angelo
Format: Electronic Conference Proceeding eBook
Language:Inglés
Published: New York : Academic Press, 1982.
Subjects:
Geometry, Differential > Congresses.
Microphysics > Congresses.
Mechanics > Congresses.
System theory > Congresses.
Mathematical physics > Congresses.
G�eom�etrie diff�erentielle > Congr�es.
Microphysique > Congr�es.
M�ecanique > Congr�es.
Th�eorie des syst�emes > Congr�es.
Physique math�ematique > Congr�es.
Geometry, Differential
Mathematical physics
Mechanics
Microphysics
System theory
Mathematische fysica.
Syst�emes, th�eorie des > Congr�es.
Congress
proceedings (reports)
Conference papers and proceedings
Conference papers and proceedings.
Actes de congr�es.
Online Access:Texto completo
Table of Contents:
  • 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 �
  • 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

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