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Celestial Encounters is for anyone
who has ever wondered about the foundations of chaos. In
1888, the 34-year-old Henri Poincare submitted a paper that
was to change the course of science, but not before it underwent
significant changes itself. "The Three-Body Problem
and the Equations of Dynamics" won a prize sponsored
by King Oscar II of Sweden and Norway and the journal Acta
Mathematica, but after accepting the prize, Poincare
found a serious mistake in his work. While correcting it,
he discovered the phenomenon of chaos.
Starting with the story of Poincare's work,
Florin Diacu and Philip Holmes trace the history of attempts
to solve the problems of celestial mechanics first posed
in Isaac Newton's Principia in 1686. In describing
how mathematical rigor was brought to bear on one of our
oldest fascinations -- the motions of the heavens -- they
introduce the people whose idea led to the flourishing field
now called nonlinear dynamics.
In presenting the modern theory of dynamical
systems, the models underlying much of modern science are
described pictorially, using the geometrical language invented
by Poincare. More generally, the authors reflect on mathematical
creativity and the roles that chance encounters, politics,
and circumstances play in it.
Florin Diacu is Associate Professor of
Mathematics at the University of Victoria in Canada. Philip
Holmes, a Fellow of the American Academy of Arts and Sciences,
is Professor of Mechanics and Applied Mathematics at Princeton
University, where he directs the Program in Applied and
Computational Mathematics.
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