有限开覆盖定理通过化“无限和运算”为“有限和运算”的方式,将一个局部成立的性质推广到在一个闭区间上整体成立。本文从整体与局部的关系分析了有限开覆盖定理的内涵,并给出具体例子分析此定理在实现整体性质与局部性质相互转化方面...有限开覆盖定理通过化“无限和运算”为“有限和运算”的方式,将一个局部成立的性质推广到在一个闭区间上整体成立。本文从整体与局部的关系分析了有限开覆盖定理的内涵,并给出具体例子分析此定理在实现整体性质与局部性质相互转化方面以及在实际问题中的应用。The finite open cover theorem extends a property that holds locally to the entire closed interval by transforming “infinite sum operations” into “finite sum operations.” This paper analyzes the essence of the finite open cover theorem from the perspective of the relationship between the global and the local. It provides concrete examples to illustrate how the theorem facilitates the mutual transformation of global and local properties, as well as its applications in practical problems.展开更多
周宏毅在论文关于Herman环与临界点中给出了三次有理函数且其临界点严格位于Herman环的边界分支的例子。该构造中主要用到临界点都位于单位圆周且保持单位圆周不动的有理函数的存在性。本文给出了一般的有理函数临界点均在单位圆周且保...周宏毅在论文关于Herman环与临界点中给出了三次有理函数且其临界点严格位于Herman环的边界分支的例子。该构造中主要用到临界点都位于单位圆周且保持单位圆周不动的有理函数的存在性。本文给出了一般的有理函数临界点均在单位圆周且保持单位圆周不动的存在性证明。同时讨论了一般显示构造的方法。In A Note on Herman, Hongyi Zhou gave an example of a cubic rational function whose critical points strictly lie on the boundary of the Herman ring. The construction mainly relies on the existence of rational functions whose critical points are located on the unit circle and keep the unit circle invariant. In this paper, we provide a general proof for the existence of rational functions whose critical points are all on the unit circle and keep the unit circle invariant. Additionally, we discuss the general methods for explicit constructions.展开更多
文摘有限开覆盖定理通过化“无限和运算”为“有限和运算”的方式,将一个局部成立的性质推广到在一个闭区间上整体成立。本文从整体与局部的关系分析了有限开覆盖定理的内涵,并给出具体例子分析此定理在实现整体性质与局部性质相互转化方面以及在实际问题中的应用。The finite open cover theorem extends a property that holds locally to the entire closed interval by transforming “infinite sum operations” into “finite sum operations.” This paper analyzes the essence of the finite open cover theorem from the perspective of the relationship between the global and the local. It provides concrete examples to illustrate how the theorem facilitates the mutual transformation of global and local properties, as well as its applications in practical problems.
文摘周宏毅在论文关于Herman环与临界点中给出了三次有理函数且其临界点严格位于Herman环的边界分支的例子。该构造中主要用到临界点都位于单位圆周且保持单位圆周不动的有理函数的存在性。本文给出了一般的有理函数临界点均在单位圆周且保持单位圆周不动的存在性证明。同时讨论了一般显示构造的方法。In A Note on Herman, Hongyi Zhou gave an example of a cubic rational function whose critical points strictly lie on the boundary of the Herman ring. The construction mainly relies on the existence of rational functions whose critical points are located on the unit circle and keep the unit circle invariant. In this paper, we provide a general proof for the existence of rational functions whose critical points are all on the unit circle and keep the unit circle invariant. Additionally, we discuss the general methods for explicit constructions.
