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Results tagged with complex-dynamics
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user 13923
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
8
votes
Roadmap to Complex Dynamics (Particularly the works of Hubbard, Douady, and Yoccoz regarding...
The Orsay notes have already been translated, but you want other references.
First read Milnor notes on external rays and local connectivity:
J. Milnor, "Periodic orbits, externals rays and the M …
- 3,081
4
votes
Fatou Coordinate for function with rationally indifferent fixed point, and repelling fixed p...
I just taught Leau's Flower Theorem today...
Your best bet to understand this map is to read Milnor's book. Click here for a copy of the original notes (which are less polished than the book). The ch …
- 3,081
4
votes
Are there some original papers or books related to applications of algebraic topology and al...
Densely scattered around the boundary of the Mandelbrot set $M$ you can find a miriad of tiny "Babybrots". We know that they are quasi-conformally isomorphic copies of $M$; that is to say, they are de …
10
votes
Accepted
Is this a Julia set (and if so, for which function family is it the Julia set)?
Your $f_\lambda$ implements Newton's method for $p_\lambda$. As you said, the zeros $\{ 1,-1,\lambda \}$ of $p_\lambda$ are fixed points of $f_\lambda$, but even more, they are superattracting fixed p …
- 3,081