Non-autonomous Julia sets with escaping critical points
Non-autonomous Julia sets with escaping critical points
复制标题
非自主朱莉娅设置了逃避临界点
DOI：
10.1080/10236198.2010.491514
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
M. Comerford
中科院分区：
文献类型：
--
作者：
M. Comerford
我们考虑非自治迭代，它是标准多项式迭代的推广，我们处理由任意选择的具有一致有界度和系数的多项式的组合序列产生的Julia集。在本文中，我们研究了所有临界点都趋近于无穷远的例子。在经典情况下，这种类型的任何例子都必须是双曲的，并且只能有一个Fatou分量，即无限远处的盆地。如果我们还要求Julia集合上的动力学是双曲的或半双曲的，这个结果在非自治情况下仍然成立。然而，一般来说，它是失败的，我们展示了三个二次多项式序列的反例，它们的临界点都逃脱了，但它们具有有界的法头分量。
We consider non-autonomous iteration which is a generalization of standard polynomial iteration where we deal with Julia sets arising from composition sequences for arbitrarily chosen polynomials with uniformly bounded degrees and coefficients. In this paper, we look at examples where all the critical points escape to infinity. In the classical case, any example of this type must be hyperbolic and there can be only one Fatou component, namely the basin at infinity. This result remains true in the non-autonomous case if we also require that the dynamics on the Julia set be hyperbolic or semi-hyperbolic. However, in general it fails and we exhibit three counterexamples of sequences of quadratic polynomials all of whose critical points escape but which have bounded Fatou components.