论文标题
轻松（水平）穿过假八块
An easy (horizontal) walk through fake octagons
论文作者
论文摘要
假八角形是一个属的两个翻译表面，只有一个单数点，与八角形相同的时期。 McMullen于2007年首次建立了许多假货的存在，更普遍地遵循所谓的等体叶的动力学特性。 本说明的目的是建立一个通过基本方法构建的明确的无限的假八ag家族。我们描述了一项简单的切割手术，并表明该手术的所有迭代都会产生假八幅。我们证明，任何迭代都会给出彼此不同的假货，我们证明，任何其他假货都可以任意地近似任何此类假货。 该注释旨在是基本的，非专家读者可以完全访问。
A fake octagon is a genus two translation surface with only one singular point and the same periods as the octagon. Existence of infinitely many fakes was first established by McMullen in 2007, and more generally follows from dynamical properties of the so called isoperiodic foliation. The purpose of this note is to build an explicit infinite family of fake octagons, constructed by means of elementary methods. We describe an easy cut-and-paste surgery and show that the all iterates of that surgery produce fake octagons. We prove that any iterate gives a fake which is different from each other, and we show that any such fake can be approximated arbitrarily well by some other fake of the family. This note is intended to be elementary and fully accessible to non-expert readers.
