All Questions
Tagged with complex-dynamics ag.algebraic-geometry
8 questions
4
votes
1
answer
298
views
Critical points of polarized endomorphisms of algebraic varieties
My main question is the following:
Let $f: \mathbb{CP}^n \to \mathbb{CP}^n$ be a holomorphic endomorphism of degree $d \ge 2$ of $\mathbb{CP}^n$ .
1. Let $X \subset \mathbb{CP}^n$ be an irreducible ...
- 293
4
votes
0
answers
150
views
Uniformization of Riemann surfaces by iso-classical Schottky groups
Let $\Gamma=<g_1, \dots, g_n>$ $\subset PGL_2(\mathbb{C})$ be a Schottky group of rank $n$. The group $\Gamma$ is called classical if there exists a set of $2n$ pairwise disjoint closed balls $\{...
- 1,042
5
votes
0
answers
216
views
Dynamical Mordell-Lang on Kahler manifolds?
Suppose that $X$ is a smooth projective variety over $\mathbb C$ and $\phi : X \to X$ is an endomorphism. Let $p \in V$ be a point and $V \subset X$ a subvariety. The dynamical Mordell-lang ...
user47305
1
vote
1
answer
476
views
Two limit cycles which lie on the same leaf
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 ...
- 356
1
vote
0
answers
113
views
Algebraic set given by sequence of polynomials
When working on some problem, I have end up with a following situation. Suppose
$P(z)=z^d+a_{d-1}z^{d-1}+\ldots+a_1z+a_0$ is a complex polynomial $d\geq2$ and that $\gamma$ and $\delta$ are non-zero ...
- 11
3
votes
0
answers
88
views
Question about a length inequality in algebraic dynamics
Let $X$ be a Noetherian scheme. Let $f\colon X\rightarrow X$ be an integral self-morphism. If $x\in X$ is a closed point, I will write $\mathcal{F}_{1}^x$ for the coherent sheaf of $\mathcal{O}_X$-...
- 3,101
17
votes
5
answers
2k
views
Arithmetic dynamics and dynamics on moduli spaces
The following question is more of a request for pointers to suitable literature on introductory material for arithmetic dynamics and dynamics on moduli spaces.
In my dissertation, I have been ...
user39719
15
votes
8
answers
4k
views
Are there some original papers or books related to applications of algebraic topology and algebraic geometry in complex dynamic systems
Recently I have much interest in algebraic topology and algebraic geometry. I am a student of the field of complex dynamical systems. According to my knowledge, my friends told me that there are many ...