Number theoretical transformations with finite range structure and their ergodic properties
type: Item
instance of: scholarly article
title: Number theoretical transformations with finite range structure and their ergodic properties
zbMATH Open document ID: 0624.10044
author: Shunji Ito
author: Michiko Yuri
published in: Tokyo Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A fibered system (B,T) is called a number-theoretical transformation with finite range structure if the set of images \(T^ nB^{(n)}\) where \(B^{(n)}\) is a cylinder of rank n forms a finite partition of B. This notion covers various complex continued fractions, Jacobi-Perron algorithm and other multidimensional maps. The paper gives sufficient conditions for the existence of \(\sigma\)-finite invariant measures and ergodicity. Furthermore the maps \[ T_ 1(x,y)=(-[-1/x]-1/x,\quad -[- y/x]-y/x)\quad and\quad T_ 2(x,y)=(-[-1/x]-1/x,\quad y/x-[y/x]) \] are given special attention. Their invariant measures are given explicitly.
reviewed by: Fritz Schweiger
Mathematics Subject Classification ID: 11K16
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 4012746
zbMATH Keywords: fibered system
zbMATH Keywords: number-theoretical transformation
zbMATH Keywords: finite range structure
zbMATH Keywords: ergodicity
zbMATH Keywords: invariant measures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270141789
OpenAlex ID: W2045030774
DOI: 10.3836/TJM/1270141789
description: scientific article; zbMATH DE number 4012746