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