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SUMMARY:Computability and Complexity of Julia Sets - Braverman\, M (Toront
 o)
DTSTART:20110601T141500Z
DTEND:20110601T151500Z
UID:TALK31620@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Studying dynamical systems is key to understanding a wide rang
 e of phenomena ranging from planetary movement to climate patterns to mark
 et dynamics. Various computational and numerical tools have been developed
  to address specific questions about dynamical systems\, such as predictin
 g the weather or planning the trajectory of a satellite. However\, the the
 ory of computation behind these problems appears to be very difficult to d
 evelop. In fact\, little is known about computability of even the most nat
 ural problems arising from dynamical systems.\n\nIn this talk I will surve
 y the recent study of the computational properties of dynamical systems th
 at arise from iterating quadratic polynomials on the complex plane. These 
 give rise to the amazing variety of fractals known as Julia sets\, and are
  closely connected to the Mandelbrot set. Julia sets are perhaps the most 
 drawn objects in Mathematics due to their fascinating fractal structure. T
 he theory behind them is even more fascinating\, and the dynamical systems
  generating them are in many ways archetypal. I will present both positive
  and negative results on the computability and computational complexity of
  Julia sets.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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