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The Transition to Chaos: The Orbit Diagram and the Mandelbrot Set
Robert L. Devaney
A publication of Science Television Productions.
Science Television Productions
1990; 60 minutes; DVD
ISBN-10: 1-878310-08-9
ISBN-13: 978-1-878310-08-8
List Price: US$25
Order Code: DVD/29
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In this lecture, Devaney explores and explains two of the most fascinating images in the study of dynamical systems: the orbit (or bifurcation) diagram, and the Mandelbrot set. Because both of these images result from iterations of quadratic functions, the level of mathematical sophistication required to understand the lecture is minimal. The main goal of the lecture is to describe the relationship between these two images, how they are generated, and what they mean mathematically. Devaney also describes several important related concepts in dynamical systems theory, including period doubling bifurcations, Feigenbaum's number, Sarkovskii's theorem, and the role of critical orbits.

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