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The terms chaos and Fractals have received widespread attention
in recent years. The alluring computer graphics images associated with these terms
have heightened interest among scientists in these ideas. This
volume contains the introductory survey lectures delivered in the American Mathematical
Short Course, Chaos and Fractals: The Mathematics Behind the Computer Graphics,
on August 6-7, 1988, given in conjunction with the AMS Centennial Meeting in Providence,
Rhode Island. In his overview, Robert L. Devaney introduces such key topics as
hyperbolicity, the period doubling route to chaos, chaotic dynamics, symbolic
dynamics and the horseshoe, and the appearance of fractals as the chaotic set
for a dynamical system. Linda Keen and Bodil Branner discuss the Mandelbrot set
and Julia sets associated to the complex quadratic family z > z*2 + c. Kathleen
T. Alligood, James A. Yorke, and Philip J. Holmes discuss some of these topics
in higher dimensional settings, including the Smale horseshoe and strange
attractors. Jenny Harrison and Michael F. Barnsley give an overview of fractal
geometry and its applications. Robert L. Devaney received
his Ph.D. from the University of California, Berkeley. He is currently Professor
of Mathematics at Boston University. His area of research interest is dynamical
systems, with specialization in Hamiltonian mechanics and complex analytic dynamics.
Linda Keen received her Ph.D. from New York University. She is currently
Professor of Mathematics at Herbert H. Lehman College, CUNY. Her areas of research
interest include the theory of Riemann surfaces, discontinuous groups, and Teichmuller
spaces, as well as complex analytic dynamical systems. |
