Ergodic properties of signed binary expansions
Ergodic properties of signed binary expansions
复制标题
有符号二进制展开式的遍历性质
DOI：
10.3934/dcds.2006.15.87
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
P. Liardet
中科院分区：
文献类型：
--
作者：
K. Dajani;C. Kraaikamp;P. Liardet
本文证明了经典符号二进制展开式主要涉及
In this paper it is shown that the classical signed binary expansion involves mainly
two dynamical systems: the binary odometer and a three state Markov chain.
Introducing the notions of additive and multiplicative block functions (e.g., sum-of-digits and Hamming
weight functions), we derive dynamical systems which are skew products over the odometer. Their spectral
properties are investigated, and applications are given to certain Maharam extensions. The proofs are related
to the spectral measure of unitary operators, obtained from cocycles associated to block functions.