Electronic ISBN:  9780821876695 
Product Code:  CONM/81.E 
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Book DetailsContemporary MathematicsVolume: 81; 1994; 270 ppMSC: Primary 58; Secondary 70;
This volume contains contributions by participants in the AMSIMSSIAM 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 threebody problem, and the artificial earth satellite. Some speakers focused on those dynamical issues—such as integrability, KAM, and extensions of the PoincaréBirkhoff 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. 
Table of Contents

Articles

Richard Moeckel  Some qualitative features of the threebody 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 PoincaréBirkhoff 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 threepoint 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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This volume contains contributions by participants in the AMSIMSSIAM 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 threebody problem, and the artificial earth satellite. Some speakers focused on those dynamical issues—such as integrability, KAM, and extensions of the PoincaréBirkhoff 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 threebody 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 PoincaréBirkhoff 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 threepoint vortex problem: commutative and noncommutative integrability [ MR 986268 ]

David L. Rod  On a theorem of Ziglin in Hamiltonian dynamics [ MR 986269 ]