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Hamiltonian dynamical systems

Edited by: Kenneth R Meyer
Available Formats:
Electronic ISBN: 978-0-8218-7669-5
Product Code: CONM/81.E
List Price: $40.00 MAA Member Price:$36.00
AMS Member Price: $32.00 Click above image for expanded view Hamiltonian dynamical systems Edited by: Kenneth R Meyer Available Formats:  Electronic ISBN: 978-0-8218-7669-5 Product Code: CONM/81.E  List Price:$40.00 MAA Member Price: $36.00 AMS Member Price:$32.00
• Book Details

Contemporary Mathematics
Volume: 811994; 270 pp
MSC: Primary 58; Secondary 70;

This volume contains contributions by participants in the AMS-IMS-SIAM Summer Research Conference on Hamiltonian Dynamical Systems, held at the University of Colorado in June 1984. The conference brought together researchers from a wide spectrum of areas in Hamiltonian dynamics. The papers vary from expository descriptions of recent developments to fairly technical presentations with new results. Collectively, they provide an excellent survey of contemporary work in this area.

The field of Hamiltonian dynamics has its roots in Newton's application of the science of dynamics to the emerging problems of orbital mechanics and in the development of celestial mechanics. Indeed, many of the talks at the conference emphasized topics directly concerned with such questions as the Newtonian $n$-body problem, the three-body problem, and the artificial earth satellite. Some speakers focused on those dynamical issues—such as integrability, KAM, and extensions of the Poincaré-Birkhoff results—that emerged from celestial mechanics and extend to wider classes of dynamical systems.

Other topics covered include periodic orbits with variation methods, twist and annulus maps, stable mainfold theory, almost periodic motion, and heteroclinic and homoclinic orbits. By bringing together papers from such a diverse range of topics, this book may serve to stimulate further development in this area.

• Articles
• Richard Moeckel - Some qualitative features of the three-body problem [ MR 986254 ]
• Donald G. Saari - Symmetry in $n$-particle systems [ MR 986255 ]
• Pau Atela - The charged isosceles $3$-body problem [ MR 986256 ]
• Dieter S. Schmidt - Central configurations in ${\bf R}^2$ and ${\bf R}^3$ [ MR 986257 ]
• Clark Robinson - Stable manifolds in Hamiltonian systems [ MR 986258 ]
• Judith M. Arms - Reduction of Hamiltonian systems for singular values of momentum [ MR 986259 ]
• John Franks - A variation on the Poincaré-Birkhoff theorem [ MR 986260 ]
• Philip Boyland - An analog of Sharkovski’s theorem for twist maps [ MR 986261 ]
• Glen R. Hall - Some problems on dynamics of annulus maps [ MR 986262 ]
• Edward E. Slaminka - Area preserving homeomorphisms of two manifolds [ MR 986263 ]
• Kenneth R. Meyer - An Anosov type stability theorem for almost periodic systems [ MR 986264 ]
• Paul H. Rabinowitz - The prescribed energy problem for periodic solutions of Hamiltonian systems [ MR 986265 ]
• Carles Simó - Homoclinic and heteroclinic phenomena in some Hamiltonian systems [ MR 986266 ]
• Philip Holmes, Jerrold Marsden and Jürgen Scheurle - Exponentially small splittings of separatrices with applications to KAM theory and degenerate bifurcations [ MR 986267 ]
• Malcolm Adams and Tudor Ratiu - The three-point vortex problem: commutative and noncommutative integrability [ MR 986268 ]
• David L. Rod - On a theorem of Ziglin in Hamiltonian dynamics [ MR 986269 ]
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Volume: 811994; 270 pp
MSC: Primary 58; Secondary 70;

This volume contains contributions by participants in the AMS-IMS-SIAM Summer Research Conference on Hamiltonian Dynamical Systems, held at the University of Colorado in June 1984. The conference brought together researchers from a wide spectrum of areas in Hamiltonian dynamics. The papers vary from expository descriptions of recent developments to fairly technical presentations with new results. Collectively, they provide an excellent survey of contemporary work in this area.

The field of Hamiltonian dynamics has its roots in Newton's application of the science of dynamics to the emerging problems of orbital mechanics and in the development of celestial mechanics. Indeed, many of the talks at the conference emphasized topics directly concerned with such questions as the Newtonian $n$-body problem, the three-body problem, and the artificial earth satellite. Some speakers focused on those dynamical issues—such as integrability, KAM, and extensions of the Poincaré-Birkhoff results—that emerged from celestial mechanics and extend to wider classes of dynamical systems.

Other topics covered include periodic orbits with variation methods, twist and annulus maps, stable mainfold theory, almost periodic motion, and heteroclinic and homoclinic orbits. By bringing together papers from such a diverse range of topics, this book may serve to stimulate further development in this area.

• Articles
• Richard Moeckel - Some qualitative features of the three-body problem [ MR 986254 ]
• Donald G. Saari - Symmetry in $n$-particle systems [ MR 986255 ]
• Pau Atela - The charged isosceles $3$-body problem [ MR 986256 ]
• Dieter S. Schmidt - Central configurations in ${\bf R}^2$ and ${\bf R}^3$ [ MR 986257 ]
• Clark Robinson - Stable manifolds in Hamiltonian systems [ MR 986258 ]
• Judith M. Arms - Reduction of Hamiltonian systems for singular values of momentum [ MR 986259 ]
• John Franks - A variation on the Poincaré-Birkhoff theorem [ MR 986260 ]
• Philip Boyland - An analog of Sharkovski’s theorem for twist maps [ MR 986261 ]
• Glen R. Hall - Some problems on dynamics of annulus maps [ MR 986262 ]
• Edward E. Slaminka - Area preserving homeomorphisms of two manifolds [ MR 986263 ]
• Kenneth R. Meyer - An Anosov type stability theorem for almost periodic systems [ MR 986264 ]
• Paul H. Rabinowitz - The prescribed energy problem for periodic solutions of Hamiltonian systems [ MR 986265 ]
• Carles Simó - Homoclinic and heteroclinic phenomena in some Hamiltonian systems [ MR 986266 ]
• Philip Holmes, Jerrold Marsden and Jürgen Scheurle - Exponentially small splittings of separatrices with applications to KAM theory and degenerate bifurcations [ MR 986267 ]
• Malcolm Adams and Tudor Ratiu - The three-point vortex problem: commutative and noncommutative integrability [ MR 986268 ]
• David L. Rod - On a theorem of Ziglin in Hamiltonian dynamics [ MR 986269 ]
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