论文标题
固定模板迭代的mandelbrot设置
Mandelbrot sets for fixed template iterations
论文作者
论文摘要
我们研究了模板迭代的动力学，这些动力学由从有限的多项式组中选择的功能的任意组成组成。特别是，我们专注于使用家族中复杂的单智图$ \ {z^d + c，c \ in \ mathbb {c}，d \ ge 2 \} $的模板。我们检查了对固定模板的连接性位点参数的依赖性，并表明，对于大多数模板，连接度轨迹在半连接中移动上限。另一方面，通常不会具有较低的半连续依赖性，我们通过反例显示了这一点。
We study the dynamics of template iterations, consisting of arbitrary compositions of functions chosen from a finite set of polynomials. In particular, we focus on templates using complex unicritical maps in the family $\{ z^d + c, c \in \mathbb{C}, d \ge 2 \}$. We examine the dependence on parameters of the connectedness locus for a fixed template and show that, for most templates, the connectedness locus moves upper semicontiuously. On the other hand, one does not in general have lower semicontinuous dependence, and we show this by means of a counterexample.
