Title | Hamiltonian Dynamical Systems [electronic resource] : History, Theory, and Applications / edited by H. S. Dumas, K. S. Meyer, D. S. Schmidt |
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Imprint | New York, NY : Springer New York, 1995 |

Connect to | http://dx.doi.org/10.1007/978-1-4613-8448-9 |

Descript | XIX, 385 p. online resource |

SUMMARY

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

CONTENT

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 -- Poincarรฉ Compactification of Hamiltonian Polynomial Vector Fields -- Transverse Homoclinic Connections for Geodesic Flows -- A New Proof of Anosovโ{128}{153}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:โ{128}{148}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

Mathematics
Mathematical analysis
Analysis (Mathematics)
Mathematics
Analysis