# Tagged Questions

Dynamics of holomorphic transformations; Mandelbrot and Julia sets.

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### Reference for instability of Newton basins of polynomials at “separation” of a multiple root

In a previous question on MO I mentioned that I had convinced myself of the following: When $f_p(z) = z - p(z)/p'(z)$ and $p$ is a complex polynomial, the Julia set, $J(f_p)$ is not continuously ...
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### Holomorphic vector field with infinite separatrix

Let $V=\sum_{i=1}^{n}a_i(z_1,\ldots z_n)\frac{\partial}{\partial z_i}$ be a holomorphic vector field defined on a neighborhood $U\subset \mathbb{C}^n$ of the origin, such that the common zero point of ...
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### reference on complex dynamics

Please someone suggest me some reference on the topic "Complex Dynamics". I want a brief geometric treatment from the root level. I have graduate level background on complex analysis, riemannian ...
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### A question on Ahlfors covering surface

Given a transcendental entire function $f$, and three Jordan domains $D_1$, $D_2$, and $D_3$ such that the closures of the three Jordan domains do not intersect with each other. Then from Ahlfors ...
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### classification of rational map with exactly only one Fatou component

We know that there exists a polynomial the Fatou set $F(P)$ is connected, which is just an attracting basin for infinity. I have a question: Given a rational function $R$ such that $F(R)$ is ...
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### Anti-Mandelbrot set

I clearly remember seeing a paper where the dynamic of the anti-conformal map $f(z)=\overline{z}^2+c$ was studied (the bar means complex conjugation). There was a picture of the analog of the ...
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