Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site petsd.UUCP
Path: utzoo!watmath!clyde!cbosgd!ihnp4!houxm!vax135!petsd!cjh
From: cjh@petsd.UUCP (Chris Henrich)
Newsgroups: net.math
Subject: Bibliography on the Mandelbrot set
Message-ID: <653@petsd.UUCP>
Date: Wed, 2-Oct-85 10:46:26 EDT
Article-I.D.: petsd.653
Posted: Wed Oct  2 10:46:26 1985
Date-Received: Thu, 3-Oct-85 06:12:47 EDT
Organization: Perkin-Elmer DSG, Tinton Falls, N.J.
Lines: 57

[]
     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.

-----------------------------------------

   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
UUCP:       ..!(cornell | ariel | ukc | houxz)!vax135!petsd!cjh
US Mail:    MS 313; Perkin-Elmer; 106 Apple St; Tinton Falls, NJ 07724
Phone:      (201) 758-7288


Brought to you by Super Global Mega Corp .com