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The Geometry of Hamiltonian Systems

Proceedings of a Workshop Held June 5–16, 1989

  • Conference proceedings
  • © 1991

Overview

Editors:
  1. Tudor Ratiu

    1. Department of Mathematics, University of California, Santa Cruz, USA
      Mathematical Sciences Research Institute, Berkeley, USA

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Part of the book series: Mathematical Sciences Research Institute Publications (MSRI, volume 22)

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Table of contents (19 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  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
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About this book

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.

Editors and Affiliations

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

    Tudor Ratiu

  • Mathematical Sciences Research Institute, Berkeley, USA

    Tudor Ratiu

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