# Tagged Questions

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### The type of a Riemann surface arising from a polynomial vector field

Consider the planar polynomial vector field $$\begin{cases} \dot x=P(x,y)\\ \dot y=Q(x,y)\end{cases}$$
It defines a singular foliation on $\mathbb{C}P^{2}$. Assume that a complex leaf contains ...

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72 views

### Generators for the affine automorphism group of the octagon

Consider an octagon $O$ with opposite edges identified. Lemma 3.2.4 of (1) (subscription link) claims that the affine automorphism group of $O$ is generated by $D_8$ and the shear $\sigma$ such that, ...

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119 views

### Computing saddle connections in flat structures

Background: A polygonal billiards table $P$ with rational angles gives rise to a flat structure $S(P)$ in a standard way, described here. Curves of constant argument on $S(P)$ which start and end at a ...

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276 views

### Strata of quadratic differentials from rational billiards

Given a quadratic differential $q$ on a surface of genus $g$, we say that $q\in \mathcal Q(k_1,\ldots,k_n)$ if $q$ has $n$ distinct zeroes of order $k_1,\ldots,k_n$ respectively. The set $\mathcal ...

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738 views

### What is the definition of ideal boundary?

In many papers about dynamical system, I found the word " ideal boundary". T don't know what is the definition of ideal boundary.