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Results tagged with complex-dynamics
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user 1162
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
4
votes
A question on Ahlfors covering surface
Yes it can, see the paper A new proof of the Ahlfors five islands theorem by Walter Bergweiler. The proof is based on a result on Nevanlinna concerning perfectly branched values, Zalcman's rescaling l …
- 2,154
8
votes
Accepted
Fixed points on Riemann surface
This theorem is an immediate consequence of a result by B. Maskit, which states that one may associate with $\Omega$ another domain $\Omega'$, conformally equivalent to $\Omega$, such that all conform …
- 2,154
10
votes
1
answer
372
views
On the conformal removability of Jordan curves
We say that a compact subset $E$ of the Riemann sphere $\mathbb{C}_\infty$ is (conformally) removable if every homeomorphism of $\mathbb{C}_\infty$ conformal outside $E$ is actually conformal everywhe …
- 2,154
7
votes
Non-locally connected polynomial Julia sets
There is a necessary and sufficient condition due to Yoccoz in terms of continued fraction expansion. The condition is that $\lambda=e^{2\pi i \theta}$ should be such that $\theta$ is not a Brjuno num …
- 2,154