On the spectrum of Farey and Gauss maps
On the spectrum of Farey and Gauss maps
复制标题
在法雷和高斯图谱上
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
S. Isola
中科院分区：
文献类型：
--
作者：
S. Isola
本文引入了由广义Borel变换和拉普拉斯变换给出的全纯函数的Hilbert空间，它们分别由Farey映射及其导出变换Gauss映射的转移算子保持不变。借助于适当的算子值幂级数，我们能够同时研究这两个算子的谱沿着与相关动力学函数的分析性质。这种构造在Mayer和Rugh先前不相关的结果之间建立了明确的联系。
In this paper we introduce Hilbert spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced transformation, the Gauss map, respectively. By means of a suitable operator-valued power series we are able to study simultaneously the spectrum of both these operators along with the analytic properties of associated dynamical ζ-functions. This construction establishes an explicit connection between previously unrelated results of Mayer and Rugh.