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VOL. 48 | 2006 Differentiable equivalence of fractional linear maps

## Abstract

A Moebius system is an ergodic fibred system $(B, T)$ (see \cite{r5}) defined on an interval $B=[a, b]$ with partition $(J_k), k \in I, \# I \geq 2$ such that $Tx = \frac{c_k + d_kx}{a_k + b_k x}$, $x \in J_k$ 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.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1132.11043
MathSciNet: MR2306204

Digital Object Identifier: 10.1214/074921706000000257

Subjects:
Primary: 37A05
Secondary: 11K55, 37E05