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Celestial Mechanics: Dedicated to Donald Saari for his 60th Birthday
Edited by: Alain Chenciner, Institute de Mécanique Céleste, Paris, France, Richard Cushman, University of Utrecht, Netherlands, and Clark Robinson and Zhihong Jeff Xia, Northwestern University, Evanston, IL
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Contemporary Mathematics
2002; 270 pp; softcover
Volume: 292
ISBN-10: 0-8218-2902-5
ISBN-13: 978-0-8218-2902-8
List Price: US$80
Member Price: US$64
Order Code: CONM/292
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See also:

Chaotic Elections! A Mathematician Looks at Voting - Donald G Saari

Hamiltonian Dynamics and Celestial Mechanics - Donald G Saari and Zhihong Xia

This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results.

This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results.

Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the \(n\)-body problem which was started by Poincari and Painlevi. Saari's solution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central configurations, his decompositions of configurational velocities, etc., are still much studied today and were reflected throughout the conference.

This volume covers various topics of current research, from central configurations to stability of periodic orbits, from variational methods to diffusion mechanisms, from the dynamics of secular systems to global dynamics of the solar systems via frequency analysis, from Hill's problem to the low energy transfer orbits and mission design in space travel, and more. This classic field of study is very much alive today and this volume offers a comprehensive representation of the latest research results.

Works by Don Saari published by the AMS include Chaotic Elections! A Mathematician Looks at Voting, ELECT, Hamiltonian Dynamics and Celestial Mechanics (Contemporary Mathematics series, Volume 198), CONM/198, and Hamiltonian Dynamical Systems (Contemporary Mathematics series, Volume 81) CONM/81.

Readership

Graduate students and research mathematicians interested in mechanics of particles and systems, dynamical systems, and ergodic theory.

Table of Contents

  • A. Albouy and J. Llibre -- Spatial central configurations for the \(1 + 4\) body problem
  • E. Belbruno -- Analytic estimation of weak stability boundaries and low energy transfers
  • F. Beukers and R. Cushman -- The complex geometry of the spherical pendulum
  • A. Chenciner -- Action minimizing periodic orbits in the Newtonian \(n\)-body problem
  • M. Corbera and J. Llibre -- On symmetric periodic orbits of the elliptic Sitnikov problem via the analytic continuation method
  • W. S. Koon, J. E. Marsden, S. D. Ross, and M. W. Lo -- Constructing a low energy transfer between Jovian moons
  • E. A. Lacomba, J. Llibre, and E. Perez-Chavela -- The generalized Sitnikov problem
  • C. Marchal -- Reflexions on the future of celestial mechanics
  • R. Moeckel -- Generic drift on Cantor sets of annuli
  • R. Montgomery -- Action spectrum and collisions in the planar three-body problem
  • P. H. Rabinowitz and E. W. Stredulinsky -- A variational shadowing method
  • C. Robinson -- Symbolic dynamics for transition tori
  • C. Simó -- Dynamical properties of the figure eight solution of the three-body problem
  • Y.-S. Sun, J.-L. Zhou, J.-Q. Zheng, and M. Valtonen -- Diffusion in comet motion
  • Q. Wang -- The Hill's region of the four-body problem
  • Z. Xia -- Some of the problems that Saari didn't solve
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