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Hamiltonian Dynamics and Celestial Mechanics
 
Edited by: Donald G. Saari Northwestern University, Evanston, IL
Zhihong Xia Northwestern University, Evanston, IL
Hamiltonian Dynamics and Celestial Mechanics
Softcover ISBN:  978-0-8218-0566-4
Product Code:  CONM/198
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7789-0
Product Code:  CONM/198.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-0566-4
eBook: ISBN:  978-0-8218-7789-0
Product Code:  CONM/198.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Hamiltonian Dynamics and Celestial Mechanics
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Hamiltonian Dynamics and Celestial Mechanics
Edited by: Donald G. Saari Northwestern University, Evanston, IL
Zhihong Xia Northwestern University, Evanston, IL
Softcover ISBN:  978-0-8218-0566-4
Product Code:  CONM/198
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7789-0
Product Code:  CONM/198.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-0566-4
eBook ISBN:  978-0-8218-7789-0
Product Code:  CONM/198.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1981996; 240 pp
    MSC: Primary 70; 58;

    This book contains selected papers from the AMS-IMS-SIAM Joint Summer Research Conference on Hamiltonian Systems and Celestial Mechanics held in Seattle in June 1995.

    The symbiotic relationship of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems.

    As one of the few books that addresses both Hamiltonian systems and celestial mechanics, this volume offers emphasis on new issues and unsolved problems. Many of the papers give new results, yet the editors purposely included some exploratory papers based on numerical computations, a section on unsolved problems, and papers that pose conjectures while developing what is known.

    Features:

    • Open research problems
    • Papers on central configurations
    Readership

    Graduate students, research mathematicians, and physicists interested in dynamical systems, Hamiltonian systems, celestial mechanics, and/or mathematical astronomy.

  • Table of Contents
     
     
    • Articles
    • Josep M. Cors and Jaume Llibre — Qualitative study of the parabolic collision restricted three-body problem [ MR 1409150 ]
    • Donald G. Saari and Zhihong Xia — Singularities in the Newtonian $n$-body problem [ MR 1409151 ]
    • Paul H. Rabinowitz — A variational approach to multibump solutions of differential equations [ MR 1409152 ]
    • Clark Robinson — Melnikov method for autonomous Hamiltonians [ MR 1409153 ]
    • Nyayapati Prem Kumar Swami — Exponentially small transversality in the rapidly forced pendulum [ MR 1409154 ]
    • Samuel R. Kaplan — The collinear one-bumper two-body problem [ MR 1409155 ]
    • Peter W. Lindstrom — Limiting mass distributions of minimal potential central configurations [ MR 1409156 ]
    • Alain Albouy — The symmetric central configurations of four equal masses [ MR 1409157 ]
    • Ernesto Perez-Chavela, Donald G. Saari, Antoni Susin and Zhiming Yan — Central configurations in the charged three body problem [ MR 1409158 ]
    • Martin Kummer — Reduction in the rotating Kepler problem and related topics [ MR 1409159 ]
    • Manuel Falconi and Ernesto A. Lacomba — Asymptotic behavior of escape solutions of mechanical systems with polynomial potentials [ MR 1409160 ]
    • Qiudong Wang — More on the heteroclinic orbits for the monotone twist maps [ MR 1409161 ]
    • Todd R. Young — Transition maps of homoclinic orbits and resonances near bifurcations of circle maps [ MR 1409162 ]
    • Xinhao Liao, Donald G. Saari and Zhihong Xia — Resonance transition and instabilities; a numerical study of the restricted three-body problem [ MR 1409163 ]
    • Samuel R. Kaplan, Richard Cushman, Sen Hu, Jaume Llibre, Christopher McCord, Donald G. Saari and Zhihong Xia — Directions of Hamiltonian dynamics and celestial mechanics [ MR 1409164 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1981996; 240 pp
MSC: Primary 70; 58;

This book contains selected papers from the AMS-IMS-SIAM Joint Summer Research Conference on Hamiltonian Systems and Celestial Mechanics held in Seattle in June 1995.

The symbiotic relationship of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems.

As one of the few books that addresses both Hamiltonian systems and celestial mechanics, this volume offers emphasis on new issues and unsolved problems. Many of the papers give new results, yet the editors purposely included some exploratory papers based on numerical computations, a section on unsolved problems, and papers that pose conjectures while developing what is known.

Features:

  • Open research problems
  • Papers on central configurations
Readership

Graduate students, research mathematicians, and physicists interested in dynamical systems, Hamiltonian systems, celestial mechanics, and/or mathematical astronomy.

  • Articles
  • Josep M. Cors and Jaume Llibre — Qualitative study of the parabolic collision restricted three-body problem [ MR 1409150 ]
  • Donald G. Saari and Zhihong Xia — Singularities in the Newtonian $n$-body problem [ MR 1409151 ]
  • Paul H. Rabinowitz — A variational approach to multibump solutions of differential equations [ MR 1409152 ]
  • Clark Robinson — Melnikov method for autonomous Hamiltonians [ MR 1409153 ]
  • Nyayapati Prem Kumar Swami — Exponentially small transversality in the rapidly forced pendulum [ MR 1409154 ]
  • Samuel R. Kaplan — The collinear one-bumper two-body problem [ MR 1409155 ]
  • Peter W. Lindstrom — Limiting mass distributions of minimal potential central configurations [ MR 1409156 ]
  • Alain Albouy — The symmetric central configurations of four equal masses [ MR 1409157 ]
  • Ernesto Perez-Chavela, Donald G. Saari, Antoni Susin and Zhiming Yan — Central configurations in the charged three body problem [ MR 1409158 ]
  • Martin Kummer — Reduction in the rotating Kepler problem and related topics [ MR 1409159 ]
  • Manuel Falconi and Ernesto A. Lacomba — Asymptotic behavior of escape solutions of mechanical systems with polynomial potentials [ MR 1409160 ]
  • Qiudong Wang — More on the heteroclinic orbits for the monotone twist maps [ MR 1409161 ]
  • Todd R. Young — Transition maps of homoclinic orbits and resonances near bifurcations of circle maps [ MR 1409162 ]
  • Xinhao Liao, Donald G. Saari and Zhihong Xia — Resonance transition and instabilities; a numerical study of the restricted three-body problem [ MR 1409163 ]
  • Samuel R. Kaplan, Richard Cushman, Sen Hu, Jaume Llibre, Christopher McCord, Donald G. Saari and Zhihong Xia — Directions of Hamiltonian dynamics and celestial mechanics [ MR 1409164 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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