AI 中文总结
研究黎曼球面上单项式非自治迭代产生的朱利亚集，通过系数和次数精确描述其相关朱利亚集，结合不变关系给出多种例子，并通过库拉托夫斯基极限阐述自治与非自治朱利亚集的联系。
AI 中文摘要
我们研究了黎曼球面上单项式非自治迭代产生的朱利亚集。依据系数和次数，对任意单项式序列相关的朱利亚集给出了精确描述。结合非自治朱利亚集的基本不变关系，在多项式非自治动力学中产生了大量显著例子，如任意基数的有限朱利亚集等。还通过库拉托夫斯基极限描述了单项式序列的自治与非自治朱利亚集之间的联系。
英文摘要
We study Julia sets arising from non-autonomous iteration of monomials on the Riemann sphere. We give a precise description of the Julia set associated to an arbitrary sequence of monomials in terms of their coefficients and degrees. Combined with the basic invariance relation for non-autonomous Julia sets, this yields a plethora of striking examples in polynomial non-autonomous dynamics: finite Julia sets of arbitrary cardinality, non-trivial Julia sets with non-empty interior, Julia sets that are perfect but not uniformly perfect, and Julia sets with empty interior but positive area. We also describe a connection between autonomous and non-autonomous Julia sets of monomial sequences through Kuratowski limits.
Comments19 pages, 1 figure
