A geometric setting for Hamiltonian perturbation theory / Anthony D. Blaom.

Format:

Book

Author/Creator:

Blaom, Anthony D., 1968- author.

Series:

Memoirs of the American Mathematical Society ; no. 727.

Memoirs of the American Mathematical Society, 0065-9266 ; number 727

Language:

English

Subjects (All):

Perturbation (Mathematics).

Hamiltonian systems.

Physical Description:

1 online resource (137 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2001]

Language Note:

English

Summary:

In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes well-known estimates of Nekhoroshev (1977), in a class of systems having almost $G$-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.

Contents:

""Contents""; ""Abstract""; ""Notation""; ""Overture""; ""Introduction""; ""Part 1. Dynamics""; ""Chapter 1. Lie-Theoretic Preliminaries""; ""Chapter 2. Action-Group Coordinates""; ""Chapter 3. On the Existence of Action-Group Coordinates""; ""Chapter 4. Naive Averaging""; ""Chapter 5. An Abstract Formulation of Nekhoroshev's Theorem""; ""Chapter 6. Applying the Abstract Nekhoroshev Theorem to Action-Group Coordinates""; ""Chapter 7. Nekhoroshev-Type Estimates for Momentum Maps""; ""Part 2. Geometry""; ""Chapter 8. On Hamiltonian G-Spaces with Regular Momenta""

""Chapter 9. Action-Group Coordinates as a Symplectic Cross-Section""""Chapter 10. Constructing Action-Group Coordinates""; ""Chapter 11. The Axisymmetric Euler-Poinsot Rigid Body""; ""Chapter 12. Passing from Dynamic Integrability to Geometric Integrability""; ""Chapter 13. Concluding Remarks""; ""Appendix A. Proof of the Nekhoroshev-Lochak Theorem""; ""Appendix B. Proof that W is a Slice""; ""Appendix C. Proof of the Extension Lemma""; ""Appendix D. An Application of Converting Dynamic Integrabilityinto Geometric Integrability: The Euler-Poinsot Rigid Body Revisited""

""Appendix E. Dual Pairs, Leaf Correspondence, and Symplectic Reduction""""Bibliography""

Notes:

"September 2001, volume 153, number 727 (third of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0320-X