# Tagged Questions

Complex dynamics is the study of dynamical systems of functions over complex numbers.

85 views

### Is every basin of attraction completely invariant?

I can't seem to find a definitive answer in the literature. I believe the answer is yes, but my focus has been on the rational maps on the Riemann sphere. At the very least I'm confident that if the ...
15 views

179 views

### Has this chaotic map been studied?

I have recently been playing around with the discrete map $$z_{n+1} = z_n - \frac{1}{z_n}$$ That is, repeatedly mapping each number to the difference between itself and its reciprocal. It shows some ...
90 views

58 views

### Convergence results for Durand-Kerner method

I've been using the mpmath library's (in Python) implementation of the Durand-Kerner method to find the roots of some "not small" polynomials (this is the polyroots function). Typically my ...
29 views

### Asymptotic values of Meromorphic map

$f(z)=\frac{e^z}{z+1}$ I know that $0$ and $\infty$ are two asymptotic values of the above function. Question:Does there exist another asymptotic values other than $0$ and $\infty$ ?
48 views

### Blow up in holomorphic dynamics

Someone could explain the concept of blow up used in holomorphic dynamics? Specifically in the context of iteration of holomorphics functions. This concept could be taken to some of the deformation ...
47 views

### More specific question on finite Blaschke products

I would like to make my previous question more precise. (1) If $B$ is a finite Blaschke product such that its Julia set $J_B$ is a Cantor subset of $S^1$ then is it true that $B$ is expanding on $J_B$...
84 views

### About growth rate of the iterated exponential on the complex plane.

Let $n$ be a positive integer. Let $f(n,x) = exp(f(n-1,x))$ and $f(0,x)=x$. Let $Q(f(n,x)) =1$ if $Re(f(n,x))<2$. Let $S(n,x) = \Sigma_{1}^{n} Q(f(n,x))$. How to estimate $S(n,2+i)$ efficiently ?
### Is the half iterate of $2\sinh(x)$ - expanded from fixed point $0$ - analytic near the real line $\mathbb{R}$?
Is the half iterate of $2\sinh(x)$ - expanded from fixed point $0$ - analytic near the real line $\mathbb{R}$? I know this function has 2 other fixed points apart from $0$, so I'm not sure. Also ...