论文标题
具有两个有限渐近值的家族函数家族的移位位点中的可访问边界点
Accessible Boundary Points in the Shift Locus of a Familiy of Meromorphic Functions with Two Finite Asymptotic Values
论文作者
论文摘要
在本文中，我们继续这项研究，始于\ cite {cjk2}，是一个具有两个渐近值，没有临界值和吸引人的固定点的杂种函数家族的分叉位点。如果我们固定固定点的乘数，则两个渐近值中的任何一个都会确定该家族的一维参数切片。我们证明，分叉基因座将此参数切片分为三个区域，两个区域类似于Mandelbrot集，一个偏移基因座，类似于Mandelbrot集的补充。在\ cite {fk，ck}中证明，分叉位点中的点对应于具有抛物线循环的函数，或者在抛物线循环的函数中，或者在极点类似dembolot brot类似于mandelbrot的双层分量的毫无疑问的边界点上。在这里，我们证明了这些点，以及在排斥周期性周期中渐近值的某些迭代点也可以从移位基因座访问。
In this paper we continue the study, began in \cite{CJK2}, of the bifurcation locus of a family of meromorphic functions with two asymptotic values, no critical values and an attracting fixed point. If we fix the multiplier of the fixed point, either of the two asymptotic values determines a one-dimensional parameter slice for this family. We proved that the bifurcation locus divides this parameter slice into three regions, two of them analogous to the Mandelbrot set and one, the shift locus, analogous to the complement of the Mandelbrot set. In \cite{FK, CK} it was proved that the points in the bifurcation locus corresponding to functions with a parabolic cycle, or those for which some iterate of one of the asymptotic values lands on a pole are accessible boundary points of the hyperbolic components of the Mandelbrot-like sets. Here we prove these points, as well as the points where some iterate of the asymptotic value lands on a repelling periodic cycle, are also accessible from the shift locus.
