Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms
type: Item
instance of: scholarly article
title: Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms
zbMATH Open document ID: 0805.11056
published in: Tokyo Journal of Mathematics
publication date: 1995-02-05T00:00:00Z
review text: R. Bowen pointed out that the boundaries of Markov partitions of hyperbolic toral automorphisms on \(T^ 3\) are not smooth. Furthermore T. Bedford has provided Markov partitions with fractal boundaries on a suitable subclass of hyperbolic toral automorphisms on \(T^ 3\), making use of the generating method of fractal curves of Dekking. The main idea is to construct a bounded domain \(X\) and a partition \(\{X_ i,i = 1,2,3\}\) on the expanding invariant plane with respect to a linear map \(L_ B^{-1}\) which induces the Markov endomorphism on \(X\) with structure matrix \(B\) by using the generating method of fractal curves. In the present paper the authors study the generating method of these domains with more accuracy.
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 558851
zbMATH Keywords: boundaries of Markov partitions
zbMATH Keywords: hyperbolic toral automorphisms
zbMATH Keywords: generating method of fractal curves
zbMATH Keywords: Markov endomorphism
author: Shunji Ito
author: Makoto Ohtsuki
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270128497
OpenAlex ID: W2067770921
DOI: 10.3836/TJM/1270128497
description: scientific article; zbMATH DE number 558851