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Contents
Preface ot the AMS Chelsea Edition xiii
Preface to the Second Edition xv
Preface to the First Edition xvii
Introduction xix
Preview xxiii
PART I PRELIMINARIES 1
Chapter 1. Differential Theory 3
Chapter 2. Calculus on Manifolds 60
PART II ANALYTICAL DYNAMICS 159
Chapter 3. Hamiltonian and Lagrandian Systems 161
Chapter 4. Hamiltonian Systems with Symmetry 253
Chapter 5. Hamilton-Jacobi Theory and mathematical Physics 370
PART III AN OUTLINE OF QUALITATIVE DYNAMICS 507
Chapter 6. Topological Dynamics 509
Chapter 7. Differentiable Dynamics 520
Chapter 8. Hamiltonian Dynamics 572
PART IV CELESTIAL MECHANICS 617
Chapter 9. The Two-Body Problem 619
Chapter 10. The Three-Body Problem 663
Appendix 741
Bibliography 759
Index 791
Glossary of Symbols 807
Errata 809