论文标题
旋转数2间隔分段仿射图
Rotation number of 2-interval piecewise affine maps
论文作者
论文摘要
我们研究了图的图表的图，其图由两个增加的片段组成，并且在扩展意义上是具有含义的。这样的地图$ f _ {\ p} $是由五五倍的$ \ p $ of meal数字满足不限制的。将$ f _ {\ p} $视为圆形映射，我们表明它具有旋转号$ρ（f _ {\ p}）$，我们计算$ \ p $在hecke-mahler系列方面的函数。作为推论，我们证明$ρ（f _ {\ p}）$是一个有理数，当$ \ p $的组件是代数数字时。
We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintuple $\p$ of real numbers satisfying inequations. Viewing $f_{\p}$ as a circle map, we show that it has a rotation number $ρ(f_{\p})$ and we compute $ρ(f_{\p})$ as a function of $\p$ in terms of Hecke-Mahler series. As a corollary, we prove that $ρ(f_{\p})$ is a rational number when the components of $\p$ are algebraic numbers.
