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> Putnam Math Competition
> Math Colloquium
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Print
Announcement
Andrew Török
University of Houston
Understanding Chaos: The Lorenz Attractor
April 7, 2014
4:15pm PGH
646
Abstract
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Studying an ordinary differential equation meant to be a simplified weather
model, Edward Lorenz discovered in 1963 an object that is called today a
strange attractor: nearby points are attracted to a set of fractal
dimension, and move around this set chaotically, with sensitive dependence
on initial conditions. Understanding this attractor was one of the 18
problems for the twenty-first century proposed in 1998 by Fields medalist
Steven Smale. Namely: "Is the dynamics of the ordinary differential
equations of Lorenz that of the geometric Lorenz attractor of Williams,
Guckenheimer, and Yorke?"
Soon thereafter Warwick Tucker answered this question in the affirmative.
His technical proof makes use of a combination of normal form theory and
validated interval arithmetic.
The talk will explain what's strange about this attractor, what Smale's
question was, models for chaos, and how approximate computations (those
done by a computer) were used to prove a mathematical theorem. Images and
computer simulations will be included.
Pizza will be served.
Click
for announcement to post
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