论文标题
多项式半群的动力学：措施，电势和外部场
Dynamics of polynomial semigroups: measures, potentials, and external fields
论文作者
论文摘要
在本文中，我们描述了与潜在理论有限生成的多项式半群（我们称为dinh-sibony措施）相关的自然不变措施。这就需要在存在外场的情况下对数电势的理论，在我们的情况下，这是通过选择一组发电机的选择明确决定的。在此过程中，我们建立了对数潜能的连续性 - 少数措施，这可能具有独立的利益。然后，我们使用MHASKAR和SAFF的$ F $功能来讨论此类Semigroups朱莉娅集合的容量和直径的界限。
In this paper, we give a description of a natural invariant measure associated with a finitely generated polynomial semigroup (which we shall call the Dinh--Sibony measure) in terms of potential theory. This requires the theory of logarithmic potentials in the presence of an external field, which, in our case, is explicitly determined by the choice of a set of generators. Along the way, we establish the continuity of the logarithmic potential for the Dinh--Sibony measure, which might be of independent interest. We then use the $F$-functional of Mhaskar and Saff to discuss bounds on the capacity and diameter of the Julia sets of such semigroups.
