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J. Wisdom (MIT)
Chaos and other insights of modern nonlinear dynamics have had a profound impact on every area of planetary dynamics. The planetary orbits evolve chaotically, the obliquity of Mars undergoes large chaotic variations, the distribution of asteroids is shaped by the underlying phase space structure, meteorites are delivered by way of chaotic zones, the Uranian satellites have passed through interesting dynamical configurations, there is diffuse chaotic transport from the Kuiper belt, and so on. Nonlinear dynamics provides a modern framework for exploring and understanding dynamical aspects of these scientific problems. But nonlinear dynamics has also given rise to new tools that significantly ease the computational tasks involved in our investigations. The symplectic mapping method was involved in all the scientific results just mentioned. The mapping method is motivated by the same insights about averaging, resonances, and chaos that have been so important in our investigation of physical dynamical systems. It is at the core of a number of widely used orbital integration packages. The mapping method, coupled with the ready availability of fast cheap workstations, has brought the investigation of the dynamics of the solar system on multi-billion-year timeframes within reach. In this lecture, I will review the historical development of the mapping method as I discuss some of the scientific problems that have driven the development of the technique.
Support from NASA Planetary Geology and Geophysics is gratefully acknowledged.
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Bulletin of the American Astronomical Society, 34, #3
© 2002. The American Astronomical Society.