Mathematical Sciences: Scientific Conference on Hamiltonian Dynamical Systems

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From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics. The power and elegance of Hamiltonian methods were first seized upon in the mid-nineteenth century by theoretical astronomers, who reduced problems in their discipline to the task of finding enough "integrals" of an appropriate Hamiltonian system; these integrals were difficult to find except for the simplest systems. Poincare showed that the emphasis should not be placed on solving the equations for a physical system, but rather that the important features of a system's behavior could be found by other means. These new methods had a strong effect on mathematics itself, as the fields of topology and dynamical systems arose out of Poincare's qualitative, geometric vision of problems in celestial mechanics and Hamiltonian systems. The qualitative approach to dynamical systems has remained an active research area, especially now that computers provide a "laboratory" in which to view systems of increasing complexity. Driven partly by the discovery in these experiments of new phenomena and partly by the maturation of the mathematical disciplines arising out of Poincare's work, the results and methods of Hamiltonian systems have grown and penetrated neighboring fields of research. This project will support an International Conference on Hamiltonian Dynamical Systems to be held from March 25-28, 1992 at the University of Cincinnati. The conference will gather together leading and newer researchers to discuss the latest results in Hamiltonian systems and its applications, and to gain an overview of how those results relate to each other and to the discipline as a whole. To emphasize the comprehensive aspect of the conference, at least one of the plenary speakers will be a professional historian of science, and will discuss the subject in the broadest possible terms.