Hamiltonian Dynamical Systems

1. Front Matter

   Pages i-xix

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2. History

   1. The Concept of Elastic Stress in Eighteenth-Century Mechanics: Some Examples from Euler

      • Craig G. Fraser

      Pages 1-14

   2. Book Two of Radical Principia

      • Bruce Pourciau

      Pages 15-37

   3. Factoring the Lunar Problem: Geometry, Dynamics, and Algebra in the Lunar Theory from Kepler to Clairaut

      • Curtis Wilson

      Pages 39-57

3. Theory and Applications

   1. A Limiting Absorption Principle for Separated Dirac Operators with Wigner von Neumann Type Potentials

      • Horst Behncke, Peter Rejto

      Pages 59-88

   2. Lax Pairs in the Henon-Heiles and Related Families

      • R. C. Churchill, G. T. Falk

      Pages 89-98

   3. Poincaré Compactification of Hamiltonian Polynomial Vector Fields

      • J. Delgado, E. A. Lacomba, J. Llibre, E. Pérez

      Pages 99-114

   4. Transverse Homoclinic Connections for Geodesic Flows

      • Victor J. Donnay

      Pages 115-125

   5. A New Proof of Anosov’s Averaging Theorem

      • H. Scott Dumas

      Pages 127-136

   6. Bifurcations in the Generalized van der Waals Interaction: The Polar Case (M = 0)

      • Antonio Elipe, Sebastián Ferrer

      Pages 137-145

   7. Energy Equipartition and Nekhoroshev-Type Estimates for Large Systems

      • Antonio Giorgilli

      Pages 147-161

   8. Suspension of Symplectic Twist Maps by Hamiltonians

      • Christophe Golé

      Pages 163-169

   9. Global Structural Stability of Planar Hamiltonian Vector Fields

      • Xavier Jarque, Jaume Llibre

      Pages 171-180

   10. Analytic Torsion, Flows and Foliations

       • Stephane Laederich

       Pages 181-193

   11. Linearized Dynamics of Symmetric Lagrangian Systems

       • Debra Lewis

       Pages 195-216

   12. A 1: —1 Semisimple Hamiltonian Hopf Bifurcation in Vortex Dynamics

       • Chjan Lim

       Pages 217-220

   13. Stability of Hamiltonian Systems over Exponentially Long Times: The Near-Linear Case

       • Pierre Lochak

       Pages 221-229

   14. Constrained Variational Principles and Stability in Hamiltonian Systems

       • John H. Maddocks, Robert L. Sachs

       Pages 231-264

   15. The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy

       • Kenneth R. Meyer, Quidong Wang

       Pages 265-282

   16. Non-Canonical Transformations of Nonlinear Hamiltonians

       • Bruce R. Miller, Vincent T. Coppola

       Pages 283-290

From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.

• bifurcation
• calculus
• dynamical systems
• hamiltonian system
• stability

• Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

  H. S. Dumas

• Institute for Dynamics Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

  K. S. Meyer

• Department of Computer Science, University of Cincinnati, Cincinnati, USA

  D. S. Schmidt

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