All Questions

I'm working with a continuous function $P: [0,1] \times W \to \mathbb{C}^n$, where $W \subset \mathbb{C}^n$ is an open, relatively compact ball centred at the origin. The map $P$ satisfies the ...

Is there a polynomial vector field on $\mathbb{C}^2$ which possesses a bounded regular leaf? By bounded, I mean a bounded subset of $\mathbb{C}^2$.

This is a naive question. Consider the Julia sets of the map $$ z \mapsto z^n + \lambda / z^k $$ with $z,\lambda \in \mathbb{C}$, and the exponents $n,k \in \mathbb{N}$. For example, for $n=k=3$, ...

Can someone suggest a book on complex geodesic flow? I am interested in it mainly because I was told these form a very useful class of Riemann surface laminations. Of special interest to me is the ...

I'm studying the dynamic of the post-critically finite for my master thesis and my professor gave me the problem concerning generalization of post-critically finite ration map. Concretely, let $f : \...

Edit 1: For a related discussion see this MSE post I apologize in advance, if this question is obvious: 1)What is an example of a polynomial vector field on $\mathbb{R}^{2}$ with at least two ...