An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
A Geometric Setting for Hamiltonian Perturbation Theory

Anthony D. Blaom Burwood, Victoria, Australia
Available Formats:
Electronic ISBN: 978-1-4704-0320-1
Product Code: MEMO/153/727.E
List Price: $57.00 MAA Member Price:$51.30
AMS Member Price: $34.20 Click above image for expanded view A Geometric Setting for Hamiltonian Perturbation Theory Anthony D. Blaom Burwood, Victoria, Australia Available Formats:  Electronic ISBN: 978-1-4704-0320-1 Product Code: MEMO/153/727.E  List Price:$57.00 MAA Member Price: $51.30 AMS Member Price:$34.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 1532001; 112 pp
MSC: Primary 70; 37;

The perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a coordinate system intrinsic to the geometry of the symmetry, we generalize and geometrize 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.

Graduate students and research mathematicians interested in topology and algebraic geometry.

• Chapters
• Introduction
• Part 1. Dynamics
• 1. Lie-theoretic preliminaries
• 2. Action-group coordinates
• 3. On the existence of action-group coordinates
• 4. Naive averaging
• 5. An abstract formulation of Nekhoroshev’s theorem
• 6. Applying the abstract Nekhoroshev theorem to action-group coordinates
• 7. Nekhoroshev-type estimates for momentum maps
• Part 2. Geometry
• 8. On Hamiltonian $G$-spaces with regular momenta
• 9. Action-group coordinates as a symplectic cross-section
• 10. Constructing action-group coordinates
• 11. The axisymmetric Euler-Poinsot rigid body
• 12. Passing from dynamic integrability to geometric integrability
• 13. Concluding remarks
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1532001; 112 pp
MSC: Primary 70; 37;

The perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a coordinate system intrinsic to the geometry of the symmetry, we generalize and geometrize 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.

Graduate students and research mathematicians interested in topology and algebraic geometry.

• Chapters
• Introduction
• Part 1. Dynamics
• 1. Lie-theoretic preliminaries
• 2. Action-group coordinates
• 3. On the existence of action-group coordinates
• 4. Naive averaging
• 5. An abstract formulation of Nekhoroshev’s theorem
• 6. Applying the abstract Nekhoroshev theorem to action-group coordinates
• 7. Nekhoroshev-type estimates for momentum maps
• Part 2. Geometry
• 8. On Hamiltonian $G$-spaces with regular momenta
• 9. Action-group coordinates as a symplectic cross-section
• 10. Constructing action-group coordinates
• 11. The axisymmetric Euler-Poinsot rigid body
• 12. Passing from dynamic integrability to geometric integrability
• 13. Concluding remarks
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.