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Terms from Chaos Theory like "the butterfly effect" and "strange
attractors" have entered popular culture, and whole movements in Poetry and
other arts have been inspired by it. The mathematics involved is called
Dynamical Systems, and at the root of the theory is the fact that solutions
to very simple equations can have very complex behaviors. I'll look at a
couple of examples in detail, and show how solutions can be visualized, how
the complexities arise mathematically, and how underlying patterns can be
found. I'll also talk (generally) about how these theories can be applied
to partial differential equations and thus geometric heat flows, in
particular discussing stability of a certain type of flow.
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