论文标题
关于复杂多项式的临界重新归一化
On critical renormalization of complex polynomials
论文作者
论文摘要
全态重新归一化在复杂多项式动力学中起重要作用。我们考虑某些条件，确保不接受多项式连接的朱莉娅集合的多项式仍然可以接收不变的连续体，在拓扑结合到较低程度的多项式上。这种不变的连续体可能包含原始多项式的额外临界点，这些点在共轭多项式的动态平面中不可见。因此，我们扩展了全态重新归一化和多项式图的概念，并描述了一个设置，其中这些概念的新广义版本适用并产生有用的拓扑结合。
Holomorphic renormalization plays an important role in complex polynomial dynamics. We consider certain conditions guaranteeing that a polynomial which does not admit a polynomial-like connected Julia set still admits an invariant continuum on which it is topologically conjugate to a lower degree polynomial. This invariant continuum may contain extra critical points of the original polynomial that are not visible in the dynamical plane of the conjugate polynomial. Thus, we extend the notions of holomorphic renormalization and polynomial-like maps and describe a setup where new generalized versions of these notions are applicable and yield useful topological conjugacies.
