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.
Inhaltsverzeichnis
History. - The Concept of Elastic Stress in Eighteenth-Century Mechanics: Some Examples from Euler. - Book Two of Radical Principia. - Factoring the Lunar Problem: Geometry, Dynamics, and Algebra in the Lunar Theory from Kepler to Clairaut. - Theory and Applications. - A Limiting Absorption Principle for Separated Dirac Operators with Wigner von Neumann Type Potentials. - Lax Pairs in the Henon-Heiles and Related Families. - Poincaré Compactification of Hamiltonian Polynomial Vector Fields. - Transverse Homoclinic Connections for Geodesic Flows. - A New Proof of Anosov s Averaging Theorem. - Bifuracation in the Generalized van der Waals Interaction: The Polar Case (M = 0). - Energy Equipartition and Nekhoroshev-Type Estimates for Large Systems. - Suspension of Symplectic Twist Maps by Hamiltonians. - Global Structural Stability of Planar Hamiltonian Vector Fields. - Analytic Torsion, Flows and Foliations. - Linearized Dynamics of Symmetric Lagrangian Systems. - A 1: 1 Semisimple Hamiltonian Hopf Bifurcation in Vortex Dynamics. - Stability of Hamiltonian Systems over Exponentially Long Times: The Near-Linear Case. - Constrained Variational Principles and Stability in Hamiltonian Systems. - The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy. - Non-canonical Transformations of Nonlinear Hamiltonians. - Linear Stability Analysis of Some Symmetrical Classes of Relative Equilibria. - Identical Maslov Indices from Different Symplectic Structures. - Discretization of Autonomous Systems and Rapid Forcing. - Computing the Motion of the Moon Accurately. - On the Rapidly Forced Pendulum. - Existence of Invariant Tori for Certain Non-Symplectic Diffeomorphisms.
