V_3的一个基本区
A Fundamental Domain for V_3
摘要：
我们描述了一个基本区穿孔黎曼曲面$V_{3,m}$参数化（莫比乌斯共轭）的二次有理映射与编号的临界点，使第一个临界点的周期为3，并使第二个临界点不映射在$m$迭代或更少的周期轨道的第一。这反过来又给出了$V_{3}$中所有III型双曲分量中所有动力学的拓扑共轭描述，并给出了$V_{3}$的拓扑模型以及其中包含的双曲分量的指示。
英文摘要：
We describe a fundamental domain for the punctured Riemann surface $V_{3,m}$ which parametrises (up to Möbius conjugacy) the set of quadratic rational maps with numbered critical points, such that the first critical point has period three, and such that the second critical point is not mapped in $m$ iterates or less to the periodic orbit of the first. This gives, in turn, a description, up to topological conjugacy, of all dynamics in all type III hyperbolic components in $V_{3}$, and gives indications of a topological model for $V_{3}$, together with the hyperbolic components contained in it.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
