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1 vote
0 answers
61 views

Holomorphic dynamical systems defined on a contractible bounded open subset of $\Bbb{C}^n$

Let $U$ be a contractible bounded open subset of $\Bbb{C}$. There is a standard classification of possible dynamical behaviors of holomorphic maps $f:U\rightarrow U$: Attracting Case: There is an ...
7 votes
1 answer
248 views

Are there such things as non-trivial entire semigroups?

I'll state the theorem I am posing up front, and then explain why I think this theorem appears to be true. I am asking if anyone can prove it, or knows references to where it is proved. Please, ...
3 votes
0 answers
84 views

Does there exist a Runge Fatou-Bieberbach in each Fatou-Bieberbach domain?

A Fatou-Bieberbach domain $\Omega \subseteq \mathbb{C}^n$ is a domain that is a proper subset of $\mathbb{C}^n$ and is biholomorphic to $\mathbb{C}^n$. A domain is said to be Runge if for each ...
4 votes
1 answer
276 views

complex dynamic system and affine algebraic variety

Let $M^n$ be a $n$-dimensional noncompact complex manifold. In "The density property for complex manifolds and geometric structures II", Dror Varolin showed that some open set of $M$ is ...
1 vote
0 answers
294 views

Can an entire function have every root function?

My question is an amalgamation of two previous questions. The first question I'd like to draw attention to is here. It asks whether there can exist a non trivial semigroup defined on $\mathbb{C}$ $$\...