论文标题
圆的分段线性同型同晶，该圆是在重新归一化的周期性的
A piecewise linear homeomorphim of the circle which is periodic under renormalization
论文作者
论文摘要
我们演示了分段线性同构$ f $ $ \ mathbb {r}/\ mathbb {z} $的存在，该坡度将理由映射到理由，其斜率是$ \ frac {2} {3} {3} $的功能，其旋转号为$ \ \ sqrt {2} $ {2} -1 $ 1-1-1这是通过证明将重新归一化过程定期应用于$ f $来实现的。我们的建筑对D. Calegari的问题给出了负面答案。当结合第二名和第三作者的作品结合使用时，我们的结果还表明，$ f _ {\ frac {2} {3}} $不会嵌入$ f $中，其中$ f _ {\ frac {2} {2} {3} {3}} $是stein-thompson $ f _ $ f _ f _} $ f _ 3} $ for a f _ f _} $ f _ 3} $ f _} $ f _ 3} $。 $ \ frac {2} {3} $。最后，我们提供了一些证据，表明对卡莱加里问题的变化有积极的答案，并记录了许多计算观察结果。
We demonstrate the existence of a piecewise linear homeomorphism $f$ of $\mathbb{R}/\mathbb{Z}$ which maps rationals to rationals, whose slopes are powers of $\frac{2}{3}$, and whose rotation number is $\sqrt{2}-1$. This is achieved by showing that a renormalization procedure becomes periodic when applied to $f$. Our construction gives a negative answer to a question of D. Calegari. When combined with work of the 2nd and 3rd authors, our result also shows that $F_{\frac{2}{3}}$ does not embed into $F$, where $F_{\frac{2}{3}}$ is the subgroup of the Stein-Thompson group $F_{2,3}$ consisting of those elements whose slopes are powers of $\frac{2}{3}$. Finally, we produce some evidence suggesting a positive answer to a variation of Calegari's question and record a number of computational observations.
