圆周上Markov映射的逆极限空间

【作者】 袁大琏；

【导师】 吕杰；

【作者基本信息】 华南师范大学 ， 应用数学， 2005， 硕士

【摘要】 §0介绍研究逆极限空间的意义,介绍对线段和图上Markov映射的逆极限空间研究的既有结果以及本文研究所得的主要结论。§1作为预备知识介绍连续统理论中关于逆极限空间的基本结论。§2利用提升引理在圆周上定义了Markov映射;特别考虑了把相邻分点之间的弧段映满圆周并环绕圆周若干次的Markov映射;给出了一类关于固定分点的Markov映射列的重要定理。§3证明了圆周上两个关于两组固定分点的Markov映射列在相同下标的两个约束映射总是关于两组分点的固定次序Markov同型的条件下生成同胚的逆极限空间;特别考虑了约束映射具有无穷个水平区间的情形;并把相应结论推广到线段上Markov映射的逆极限空间。更多还原

【Abstract】 In §0 we introduce the significance of inverse limit spaces research, some known results on inverse limit spaces on intervals or graphs and the main results of our research. In §1 we introduce as preparative knowledge the basic continuum theory of inverse limit spaces. In §2 we define Markov maps on S~1 through lifts on R while the Markov maps which take an arc between two adjacent partition points onto the circle and make it surround the circle several times are taken into special consider. We also give an important theorem on a kind of inverse sequences of Markov maps on the circle with respect to a fixed partition. In §3 we prove that two sequences of Markov maps on the circle generated homeomorphic inverse limit spaces if each pair of the bounding maps with the same subscript are of the same Markov type with respect to a fixed arrangement of the two partitions. Here we allow the bounding maps to have infinitely many horizontal intervals. The relative conclusions are extended to the inverse limit spaces of interval Markov maps.更多还原