分式线性映射的可微等价性
Differentiable equivalence of fractional linear maps
摘要：
Moebius系统是定义在具有分区$(J_k),k\in I,#I\geq 2$的区间$B=[a,b]$上的遍历遍历系统$(B,T)$（参见\citer 5），使得$Tx=\frac{c_k+d_kx}{a_k+b_kx}$、$x\in J_k$和$T|_{J_k}$是从$J_k$到$B$的双射映射。众所周知，对于$#I=2$，不变密度可以写成$h(x)=\int_{B^*}\frac{dy}{(1+xy)^2}$的形式，其中$B^*$是合适的区间。该结果不适用于$#I\geq 3$。然而，在本文中的$#I=3$两类区间映射的确定，允许上述结果的扩展。
英文摘要：
A Moebius system is an ergodic fibred system $(B,T)$ (see \citer5) defined on an interval $B=[a,b]$ with partition $(J_k),k\in I,#I\geq 2$ such that $Tx=\frac{c_k+d_kx}{a_k+b_kx}$, $x\in J_k$ and $T|_{J_k}$ is a bijective map from $J_k$ onto $B$. It is well known that for $#I=2$ the invariant density can be written in the form $h(x)=\int_{B^*}\frac{dy}{(1+xy)^2}$ where $B^*$ is a suitable interval. This result does not hold for $#I\geq 3$. However, in this paper for $#I=3$ two classes of interval maps are determined which allow the extension of the before mentioned result.
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。
