Fundamental Dichotomy

Robert P. Munafo, 2000 Feb 7.

A theorem of complex dynamics, proven by Fatou and Julia in 1919.

Every Julia set is either a connected set or a Cantor set. That is, every Julia set either has one piece, or an infinite number of pieces, equal in number to the continuum.

You can determine which it is by iterating from the critical point z=0. This is equivalent to finding out if z is in the Mandelbrot set.


From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index

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