论文标题
Mandelbrot集的手术序列和自相似性
Surgery sequences and self-similarity of the Mandelbrot set
论文作者
论文摘要
我们在克莱尼亚群体理论的双曲线dehn手术思想的理性图中介绍了一个类似图。手术序列是一系列限制后有限的图（精确方式），以限制后有限的有限映射，其中至少一个严格的前碘临界轨道。作为这个想法的应用，我们给出了Tan Lei定理的新的基本证明，内容涉及Julia集的渐近性自相似性和Misiurewicz点的Mandelbrot。
We introduce an analog in the context of rational maps of the idea of hyperbolic Dehn surgery from the theory of Kleinian groups. A surgery sequence is a sequence of postcritically finite maps limiting (in a precise manner) to a postcritically finite map with at least one strictly preperiodic critical orbit. As an application of this idea we give a new and elementary proof of Tan Lei's theorem on the asymptotic self-similarity of Julia Sets and the Mandelbrot Set at Misiurewicz points.
