Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equidistribution for matings of quadratic maps with the Modular group   We study the asymptotic behavior of the family of holomorphic correspondences
$\lbrace\mathcal{F}_a\rbrace_{a\in\mathcal{K}}$, given by
$$\left(\frac{az+1}{z+1}\right)^2+\left(\frac{az+1}{z+1}\right)\left(\frac{aw-1}{w-1}\right)+\left(\frac{aw-1}{w-1}\right)^2=3.$$
It was proven by Bullet and Lomonaco that $\mathcal{F}_a$ is a mating between
the modular group $\operatorname{PSL}_2(\mathbb{Z})$ and a quadratic rational
map. We show for every $a\in\mathcal{K}$, the iterated images and preimages
under $\mathcal{F}_a$ of nonexceptional points equidistribute, in spite of the
fact that $\mathcal{F}_a$ is weakly-modular in the sense of Dinh, Kaufmann and
Wu but it is not modular. Furthermore, we prove that periodic points
equidistribute as well.

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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat