cjh@petsd.UUCP (Chris Henrich) (10/02/85)
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This is essentially a re-posting of an article I sent out
last year. I think it is appropriate, because of renewed
interest on the net regarding the Mandelbrot set.
This is a bibliography of interesting articles on the
Mandelbrot set and related topics.
1. Blanshard, Paul.
Complex analytic dynamics on the Riemann sphere.
Bull. Amer. Math. Soc. 11 # 1, July 1984, 85-142.
This is a good introduction to the technical side of the
subject.
2. Douady, A.
Syste`mes dynamiques holomorphes.
Se'minaire Bourbaki, 35, 1982-1983, No. 599.
(Also published in the periodical Asterisque)
This goes deeper into the structure of the Mandelbrot set,
in particular it explains why the construction described in
Dewdeney's article in _Scientific_American_ actually gives the
Mandelbrot set.
3. Douady, A.; Hubbard, J.
Ite'ration des polyno^mes quadratiques complexes.
Comtes Rendus Acad. Sci. Paris Section A, vol. 294,
1982, 123-126.
The proof that the Mandelbrot set is connected. Not
light reading.
4. Mandelbrot, B.
Fractal aspects of the iteration of z --> <lambda> z ( 1 - z ),
Ann. New York Acad. Sci. 357 (1980), 249-259.
5. Peitgen, H. O.; Saupe, D.; Haeseler, F. v.
Cayley's problem and Julia sets.
Math. Intelligencer 6 # 2, 1984, 11-20.
Good graphics, describing the Julia sets for several other
maps than those of the form z -> z*z + c.
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BTW, thanks to Joe Buck for showing how to prove that if
|z| gets larger than 2 it will tend to infinity.
Regards,
Chris
--
Full-Name: Christopher J. Henrich
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