Brolin's Theorem for curves in two complex dimensions

A generalization of the converse of Brolin's theorem

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

塞尔伯格与布林关于复动力学值分布的研究

Selberg and Brolin on value distribution of complex dynamics

本文指出先前研究已得出了布林-吕伯奇等分布定理的更优量化，并在假设H的指数版本下得到了吕伯奇定理的量化。

On Brolin's theorem over the quaternions

In this paper we investigate the Brolin's theorem over $\mathbb{H}$, the skew field of quaternions. Moreover, considering a quaternionic polynomial $p$ with real coefficients, we focus on the properties of its equilibrium measure, among the others, the mixing property and the Lyapunov exponents of the measure. We prove a central limit theorem and we compute the topological entropy and measurable entropy with respect to the quaternionic equilibrium measure. We prove that they are equal considering both a quaternionic polynomial with real coefficients and a polynomial with coefficients in a slic…

Theoreme d'equidistribution de Brolin en dynamique p-adique

We prove an analog of the famous equidistribution theorem of Brolin for rational mappings in one variable defined over the p-adic field C_p. We construct a mixing invariant probability measure which describes the asymptotic distribution of iterated preimages of a given point. This measure is supported on the Berkovich space associated to the projective line over C_p. We show that its support is precisely the Julia set as defined by Rivera-Letelier. Our results are based on the construction of a Laplace operator on real trees with arbitrary number of branching as done by Favre-Jonsson.

The dynamics of holomorphic correspondences of P^1: invariant measures and the normality set

This paper is motivated by Brolin's theorem. The phenomenon we wish to demonstrate is as follows: if $F$ is a holomorphic correspondence on $\mathbb{P}^1$, then (under certain conditions) $F$ admits a measure $μ_F$ such that, for any point $z$ drawn from a "large" open subset of $\mathbb{P}^1$, $μ_F$ is the weak*-limit of the normalised sums of point masses carried by the pre-images of $z$ under the iterates of $F$. Let ${}^\dagger{F}$ denote the transpose of $F$. Under the condition $d_{top}(F) > d_{top}({}^\dagger{F})$, where $d_{top}$ denotes the topological degree, the above phenomemon was…

动力学Fekete-Szegő定理

A Dynamical Fekete-Szegő Theorem

本文研究了紧集E的动力学Fekete-Szegő定理，证明了代数多项式生成的填充Julia集在特定拓扑下收敛，并给出了Rumely高度的动态对应。