Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Integrable Systems: A Celebration of Emma Previato’s 65th Birthday
- 1 Trace Ideal Properties of a Class of Integral Operators
- 2 Explicit Symmetries of the Kepler Hamiltonian
- 3 A Note on the Commutator of Hamiltonian Vector Fields
- 4 Nodal Curves and a Class of Solutions of the Lax Equation for Shock Clustering and Burgers Turbulence
- 5 Solvable Dynamical Systems in the Plane with Polynomial Interactions
- 6 The Projection Method in Classical Mechanics
- 7 Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets
- 8 Bi-Flat F-Manifolds: A Survey
- 9 The Periodic 6-Particle Kac-van Moerbeke System
- 10 Integrable Mappings from a Unified Perspective
- 11 On an Arnold-Liouville Type Theorem for the Focusing NLS and the Focusing mKdV Equations
- 12 Commuting Hamiltonian Flows of Curves in Real Space Forms
- 13 The Kowalewski Top Revisited
- 14 The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem
- 15 Tropical Markov Dynamics and Cayley Cubic
- 16 Positive One–Point Commuting Difference Operators∗†
2 - Explicit Symmetries of the Kepler Hamiltonian
Published online by Cambridge University Press: 19 March 2020
Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Integrable Systems: A Celebration of Emma Previato’s 65th Birthday
- 1 Trace Ideal Properties of a Class of Integral Operators
- 2 Explicit Symmetries of the Kepler Hamiltonian
- 3 A Note on the Commutator of Hamiltonian Vector Fields
- 4 Nodal Curves and a Class of Solutions of the Lax Equation for Shock Clustering and Burgers Turbulence
- 5 Solvable Dynamical Systems in the Plane with Polynomial Interactions
- 6 The Projection Method in Classical Mechanics
- 7 Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets
- 8 Bi-Flat F-Manifolds: A Survey
- 9 The Periodic 6-Particle Kac-van Moerbeke System
- 10 Integrable Mappings from a Unified Perspective
- 11 On an Arnold-Liouville Type Theorem for the Focusing NLS and the Focusing mKdV Equations
- 12 Commuting Hamiltonian Flows of Curves in Real Space Forms
- 13 The Kowalewski Top Revisited
- 14 The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem
- 15 Tropical Markov Dynamics and Cayley Cubic
- 16 Positive One–Point Commuting Difference Operators∗†
Summary
Using quaternions, we give explicit formulas for the global symmetries of the three-dimensional Kepler problem. The regularizations of the Kepler problem that are based on the Hopf map and on stereographic projections, respectively, are interpreted in terms of these symmetries.
Keywords
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- Chapter
- Information
- Integrable Systems and Algebraic Geometry , pp. 38 - 56Publisher: Cambridge University PressPrint publication year: 2020