论文标题
一种计算圆圈旋转数的算法
An Algorithm to compute Rotation Numbers in the circle
论文作者
论文摘要
在本文中，我们提出了一种有效的算法来计算第一度的圆形图的旋转间隔。它基于具有恒定截面的单调圆图的旋转数量的计算。该算法的主要强度是它计算\ emph {priction}连续不可逆转度的一个圆形图的自然子类的旋转间隔。 我们还通过绘制一个参数的地图家族的魔鬼楼梯以及一些特殊的非差异家庭的魔鬼家族和旋转间隔来比较其他现有算法，其中大多数是围绕围绕不同的地图的现有算法的范围。
In this article we present an efficient algorithm to compute rotation intervals of circle maps of degree one. It is based on the computation of the rotation number of a monotone circle map of degree one with a constant section. The main strength of this algorithm is that it computes \emph{exactly} the rotation interval of a natural subclass of the continuous non-invertible degree one circle maps. We also compare our algorithm with other existing ones by plotting the Devil's Staircase of a one-parameter family of maps and the Arnold Tongues and rotation intervals of some special non-differentiable families, most of which were out of the reach of the existing algorithms that were centred around differentiable maps.
