# American Institute of Mathematical Sciences

December  2008, 1(4): i-i. doi: 10.3934/dcdss.2008.1.4i

## Preface

 1 UAM-ztapalapa, Dpto. de Matematicas, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico D.F. 09340, Mexico 2 Department of Mathematics, Northwestern University, Evanston IL 60208 3 Department of Mathematics, Northeastern Illinois University, Chicago, IL 60625

Published  September 2008

This special issue of DCDS-S is in honor of the contribution of Donald Saari to the mathematical aspects of Celestial Mechanics over a period of 40 years. He had important contributions to the classification of the $n$-body problem as time goes to infinity, the measure of the set of initial conditions leading to collision, singularities that are not collisions for the $n$-body problem, and many other topics. Years ago, he made a conjecture about whether a system with constant moment of inertia must be a planar relative equilibrium. (See Saari's article in this issue for a further explanation.) This problem has been solved just for the three body problem and is still open for $n \geq 4$r. Several of the articles in this issue deal with this issue and related issues about central configurations (a generalization of relative equilibria). The recent monograph (D. Saari, "Collisions, rings, and other Newtonian $N$-body problems", CBMS Region Conference in Mathematics 104(2005), Amer. Math. Soc., Providence RI) gives an introduction into the full extent of the Saari's contribution to celestial mechanics. Besides the creative ideas Don brought to his work, his clear and inspiring talks and exposition has contributed to his impact on the field. We are sure that all the contributors to this issue join us in thanking Don for his contributions and inspiration to us all.
The idea for this collection of papers related to the work of Saari originated at the Saarifest Conference held in 2005 in Guanajuato México. The papers in this collection vary between many that relate rather closely to the work of Saari to others that relate to his work in a broad sense. We hope that you the reader benefit from the work presented here and you are inspired to study some of his original papers and monographs.
Citation: Ernesto Perez Chavela, Clark Robinson, Marian Gidea. Preface. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : i-i. doi: 10.3934/dcdss.2008.1.4i
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