Ebook: Hamiltonian Dynamical Systems: History, Theory, and Applications

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.

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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.

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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:
Front Matter....Pages i-xix
The Concept of Elastic Stress in Eighteenth-Century Mechanics: Some Examples from Euler....Pages 1-14
Book Two of Radical Principia....Pages 15-37
Factoring the Lunar Problem: Geometry, Dynamics, and Algebra in the Lunar Theory from Kepler to Clairaut....Pages 39-57
A Limiting Absorption Principle for Separated Dirac Operators with Wigner von Neumann Type Potentials....Pages 59-88
Lax Pairs in the Henon-Heiles and Related Families....Pages 89-98
Poincar? Compactification of Hamiltonian Polynomial Vector Fields....Pages 99-114
Transverse Homoclinic Connections for Geodesic Flows....Pages 115-125
A New Proof of Anosov’s Averaging Theorem....Pages 127-136
Bifurcations in the Generalized van der Waals Interaction: The Polar Case (M = 0)....Pages 137-145
Energy Equipartition and Nekhoroshev-Type Estimates for Large Systems....Pages 147-161
Suspension of Symplectic Twist Maps by Hamiltonians....Pages 163-169
Global Structural Stability of Planar Hamiltonian Vector Fields....Pages 171-180
Analytic Torsion, Flows and Foliations....Pages 181-193
Linearized Dynamics of Symmetric Lagrangian Systems....Pages 195-216
A 1: —1 Semisimple Hamiltonian Hopf Bifurcation in Vortex Dynamics....Pages 217-220
Stability of Hamiltonian Systems over Exponentially Long Times: The Near-Linear Case....Pages 221-229
Constrained Variational Principles and Stability in Hamiltonian Systems....Pages 231-264
The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy....Pages 265-282
Non-Canonical Transformations of Nonlinear Hamiltonians....Pages 283-290
Linear Stability Analysis of Some Symmetrical Classes of Relative Equilibria....Pages 291-317
Identical Maslov Indices from Different Symplectic Structures....Pages 319-327
Discretization of Autonomous Systems and Rapid Forcing....Pages 329-340
Computing the Motion of the Moon Accurately....Pages 341-361
On the Rapidly Forced Pendulum....Pages 363-372
Existence of Invariant Tori for Certain Non-Symplectic Diffeomorphisms....Pages 373-385

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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:
Front Matter....Pages i-xix
The Concept of Elastic Stress in Eighteenth-Century Mechanics: Some Examples from Euler....Pages 1-14
Book Two of Radical Principia....Pages 15-37
Factoring the Lunar Problem: Geometry, Dynamics, and Algebra in the Lunar Theory from Kepler to Clairaut....Pages 39-57
A Limiting Absorption Principle for Separated Dirac Operators with Wigner von Neumann Type Potentials....Pages 59-88
Lax Pairs in the Henon-Heiles and Related Families....Pages 89-98
Poincar? Compactification of Hamiltonian Polynomial Vector Fields....Pages 99-114
Transverse Homoclinic Connections for Geodesic Flows....Pages 115-125
A New Proof of Anosov’s Averaging Theorem....Pages 127-136
Bifurcations in the Generalized van der Waals Interaction: The Polar Case (M = 0)....Pages 137-145
Energy Equipartition and Nekhoroshev-Type Estimates for Large Systems....Pages 147-161
Suspension of Symplectic Twist Maps by Hamiltonians....Pages 163-169
Global Structural Stability of Planar Hamiltonian Vector Fields....Pages 171-180
Analytic Torsion, Flows and Foliations....Pages 181-193
Linearized Dynamics of Symmetric Lagrangian Systems....Pages 195-216
A 1: —1 Semisimple Hamiltonian Hopf Bifurcation in Vortex Dynamics....Pages 217-220
Stability of Hamiltonian Systems over Exponentially Long Times: The Near-Linear Case....Pages 221-229
Constrained Variational Principles and Stability in Hamiltonian Systems....Pages 231-264
The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy....Pages 265-282
Non-Canonical Transformations of Nonlinear Hamiltonians....Pages 283-290
Linear Stability Analysis of Some Symmetrical Classes of Relative Equilibria....Pages 291-317
Identical Maslov Indices from Different Symplectic Structures....Pages 319-327
Discretization of Autonomous Systems and Rapid Forcing....Pages 329-340
Computing the Motion of the Moon Accurately....Pages 341-361
On the Rapidly Forced Pendulum....Pages 363-372
Existence of Invariant Tori for Certain Non-Symplectic Diffeomorphisms....Pages 373-385
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