论文标题
非线性分段合同图的周期结构
Periodic structures for nonlinear piecewise contracting maps
论文作者
论文摘要
在本文中，我们首先表明，任何非线性单调增加的合同地图都在一个单位间隔上与一个不连续点，其独特的周期性点具有$ n $ conjugates to $ n $ conjugates到分段线性收缩地图，该地图具有同一时期的定期点。其次，我们考虑一个单调增加合同图的参数家族，并表明该家族具有与Farey系列相关的参数的周期性结构，称为Arnold舌头。这意味着存在具有正面lebesgue度量的参数集，使得地图具有任意时期的周期点。此外，具有$（m+n）$的参数集存在于$ m $和$ n $的参数集之间。
In this paper, we first show that any nonlinear monotonic increasing contracting maps with one discontinuous point on a unit interval which has an unique periodic point with period $n$ conjugates to a piecewise linear contracting map which has periodic point with same period. Second, we consider one parameter family of monotonic increasing contracting maps, and show that the family has the periodic structure called Arnold tongue for the parameter which is associated with the Farey series. This implies that there exist a parameter set with a positive Lebesgue measure such that the map has a periodic point with an arbitrary period. Moreover, the parameter set with period $(m+n)$ exists between the parameter set with period $m$ and $n$.
