论文标题
关于带有固定乘数的Cubic多项式的Siegel磁盘的大小
On the size of Siegel disks with fixed multiplier for cubic polynomials
论文作者
论文摘要
我们研究了立方多项式的参数空间的切片，其中我们将固定点的乘数固定为一些值$λ$。这里感兴趣的主要对象是线性化参数化收敛的半径。其对数的相反是该参数的亚谐波功能，其laplacian $μ_λ$特别感兴趣。在情况下，我们将其支持与Zakeri曲线相关联，乘数是中性的，具有界面类型的非理性旋转数。在吸引情况下，我们使用Petersen和Tan的作品来定义和研究Zakeri曲线的类似物。在抛物线情况下，我们使用渐近尺寸的概念定义了一个类似物。我们证明了$μ_{λ_n} $的收敛定理，to $μ_λ$ for $λ_n= \ exp（2πip_n/q_nn）$和$λ= \ exp（2πiθ）$，其中$θ$是界限不理性的，$ p_n/q_n/q_n/q_n/q_n $。
We study the slices of the parameter space of cubic polynomials where we fix the multiplier of a fixed point to some value $λ$. The main object of interest here is the radius of convergence of the linearizing parametrization. The opposite of its logarithm turns out to be a sub-harmonic function of the parameter whose Laplacian $μ_λ$ is of particular interest. We relate its support to the Zakeri curve in the case the multiplier is neutral with a bounded type irrational rotation number. In the attracting case, we define and study an analogue of the Zakeri curve, using work of Petersen and Tan. In the parabolic case, we define an analogue using the notion of asymptotic size. We prove a convergence theorem of $μ_{λ_n}$ to $μ_λ$ for $λ_n= \exp(2πi p_n/q_nn)$ and $λ= \exp(2πiθ)$ where $θ$ is a bounded type irrational and $p_n/q_n$ are its convergents.
