The Kepler Problem

1. Front Matter

   Pages i-xvii

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2. Introductory Survey

   1. Introductory Survey

      • Bruno Cordani

      Pages 1-16

3. Elementary Theory

   1. Front Matter

      Pages 17-17

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   2. Basic Facts

      • Bruno Cordani

      Pages 18-35

   3. Separation of Variables and Action-Angle Coordinates

      • Bruno Cordani

      Pages 36-60

   4. Quantization of the Kepler Problem

      • Bruno Cordani

      Pages 61-95

   5. Regularization and Symmetry

      • Bruno Cordani

      Pages 96-107

4. Group-Geometric Theory

   1. Front Matter

      Pages 109-109

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   2. Conformal Regularization

      • Bruno Cordani

      Pages 110-142

   3. Spinorial Regularization

      • Bruno Cordani

      Pages 143-160

   4. Return to Separation of Variables

      • Bruno Cordani

      Pages 161-191

   5. Geometric Quantization

      • Bruno Cordani

      Pages 192-210

   6. Kepler Problem with Magnetic Monopole

      • Bruno Cordani

      Pages 211-234

5. Perturbation Theory

   1. Front Matter

      Pages 235-235

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   2. General Perturbation Theory

      • Bruno Cordani

      Pages 236-267

   3. Perturbations of the Kepler Problem

      • Bruno Cordani

      Pages 268-292

   4. Perturbations with Axial Symmetry

      • Bruno Cordani

      Pages 293-319

6. Back Matter

   Pages 321-439

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Because of the correspondences existing among all levels of reality, truths pertaining to a lower level can be considered as symbols of truths at a higher level and can therefore be the "foundation" or support leading by analogy to a knowledge of the latter. This confers to every science a superior or "elevating" meaning, far deeper than its own original one. - R. GUENON, The Crisis of Modern World Having been interested in the Kepler Problem for a long time, I have al­ ways found it astonishing that no book has been written yet that would address all aspects of the problem. Besides hundreds of articles, at least three books (to my knowledge) have indeed been published al­ ready on the subject, namely Englefield (1972), Stiefel & Scheifele (1971) and Guillemin & Sternberg (1990). Each of these three books deals only with one or another aspect of the problem, though. For example, En­ glefield (1972) treats only the quantum aspects, and that in a local way. Similarly, Stiefel & Scheifele (1971) only considers the linearization of the equations of motion with application to the perturbations of celes­ tial mechanics. Finally, Guillemin & Sternberg (1990) is devoted to the group theoretical and geometrical structure.

• Boundary value problem
• Mathematical physics
• Minkowski space
• Potential
• astrophysics
• differential geometry theory

"This is an interesting book, which well organizes the group-geometric aspects of the Kepler problem on which a great number of articles have been published along with the advance of symmetry theory. . . . a nice reference not only for graduate students but also for scientists who are interested in dynamical systems with symmetry." --MathSciNet

• Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

  Bruno Cordani

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