Romik动力系统的数论性质
Number theoretical properties of Romik's dynamical system
摘要：
我们研究了一个动力系统，它最初是由Romik在2008年使用Berggren关于毕达哥拉斯三元组的旧定理定义的。Romik的系统与单位区间上的Farey映射密切相关，Farey映射产生了一个加性连分数算法。我们探讨了Romik系统的一些数论性质。特别是，我们证明了一个类似的拉格朗日定理的情况下的Romik系统的单位四分之一圆，其中指出，一个点具有最终周期的数字扩展当且仅当该点被定义在一个真正的二次扩域的理性。
英文摘要：
We study a dynamical system that was originally defined by Romik in 2008 using an old theorem of Berggren concerning Pythagorean triples. Romik's system is closely related to the Farey map on the unit interval which generates an additive continued fraction algorithm. We explore some number theoretical properties of the Romik system. In particular, we prove an analogue of Lagrange's theorem in the case of the Romik system on the unit quarter circle, which states that a point possesses an eventually periodic digit expansion if and only if the point is defined over a real quadratic extension field of rationals.
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。
