The Geometry of Hamiltonian Systems

1. Front Matter

   Pages i-x

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2. Heisenberg Algebras, Grassmannians and Isospectral Curves

   • Malcolm R. Adams, Maarten Bergvelt

   Pages 1-7

3. Coadjoint Orbits, Spectral Curves and Darboux Coordinates

   • M. R. Adams, J. Harnad, J. Hurtubise

   Pages 9-21

4. Hamiltonian Systems on the Jacobi Varieties

   • Solomon J. Alber

   Pages 23-32

5. A Universal Reduction Procedure for Hamiltonian Group Actions

   • Judith M. Arms, Richard H. Cushman, Mark J. Gotay

   Pages 33-51

6. Linear Stability of a Periodic Orbit in the System of Falling Balls

   • Jian Cheng, Maciej P. Wojtkowski

   Pages 53-71

7. Birth and Death of Invariant Tori for Hamiltonian Systems

   • Luigi Chierchia

   Pages 73-80

8. Dynamical Aspects of the Bidiagonal Singular Value Decomposition

   • Percy Deift, James Demmel, Luen-Chau Li, Carlos Tomei

   Pages 81-96

9. The Rhomboidal Four Body Problem. Global Flow on the Total Collision Manifold

   • J. Delgado-Fernández, E. Pérez-Chavela

   Pages 97-110

10. Toward a Topological Classification of Integrable PDE’s

    • Nicholas M. Ercolani, David W. McLaughlin

    Pages 111-129

11. Topological Classification of All Integrable Hamiltonian Differential Equations of General Type With Two Degrees of Freedom

    • A. T. Fomenko

    Pages 131-339

12. Monotone Maps of \({\mathbb{T}^n}\) × ∝ⁿ and Their Periodic Orbits

    • Christophe Golé

    Pages 341-366

13. A Lower Bound for the Number of Fixed Points of Orientation Reversing Homeomorphisms

    • Krystyna Kuperberg

    Pages 367-371

14. Invariant Tori and Cylinders for a Class of Perturbed Hamiltonian Systems

    • Ernesto A. Lacomba, Jaume Llibre, Ana Nunes

    Pages 373-385

15. Modified Structures Associated with Poisson Lie Groups

    • Luen-Chau Li, Serge Parmentier

    Pages 387-401

16. Optimal Control of Deformable Bodies and Its Relation to Gauge Theory

    • R. Montgomery

    Pages 403-438

17. The Augmented Divisor and Isospectral Pairs

    • Randolph James Schilling

    Pages 439-461

18. Symplectic Numerical Integration of Hamiltonian Systems

    • Clint Scovel

    Pages 463-496

19. Connections Between Critical Points in the Collision Manifold of the Planar 3-Body Problem

    • C. Simó, A. Susín

    Pages 497-518

20. The Non-collision Sigularities of the 5 body Problem

    • Zhihong Xia

    Pages 519-527

The papers in this volume are an outgrowth of the lectures and informal discussions that took place during the workshop on "The Geometry of Hamiltonian Systems" which was held at MSRl from June 5 to 16, 1989. It was, in some sense, the last major event of the year-long program on Symplectic Geometry and Mechanics. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, and dynamical systems in general. The organizers of the conference were R. Devaney (co-chairman), H. Flaschka (co-chairman), K. Meyer, and T. Ratiu. The entire meeting was built around two mini-courses of five lectures each and a series of two expository lectures. The first of the mini-courses was given by A. T. Fomenko, who presented the work of his group at Moscow University on the classification of integrable systems. The second mini­ course was given by J. Marsden of UC Berkeley, who spoke about several applications of symplectic and Poisson reduction to problems in stability, normal forms, and symmetric Hamiltonian bifurcation theory. Finally, the two expository talks were given by A. Fathi of the University of Florida who concentrated on the links between symplectic geometry, dynamical systems, and Teichmiiller theory.

• differential equation
• dynamical systems
• gauge theory
• manifold
• symplectic geometry

• Department of Mathematics, University of California, Santa Cruz, USA

  Tudor Ratiu

• Mathematical Sciences Research Institute, Berkeley, USA

  Tudor Ratiu