Bowen-Franks groups of reducible bimodal subshifts of finite type
type: Item
instance of: scholarly article
title: Bowen-Franks groups of reducible bimodal subshifts of finite type
zbMATH Open document ID: 1104.37007
author: N. E. Zubov
published in: Linear Algebra and its Applications
publication date: 2006-03-29T00:00:00Z
review text: Here, bimodal maps are considered. It is assumed that the critical points are periodic. Hence, using a suitable partition into intervals, the bimodal map has the Markov property, and therefore it is conjugate to a subshift of finite type. From the transition matrix one can calculate the Bowen-Franks group of the map. In [\textit{N.~Martins}, \textit{R.~Severino} and \textit{J.~Sousa Ramos}, J. Difference Equ. Appl. 9, 423--433 (2003; Zbl 1018.37008)], an explicit formula for the Bowen-Franks group involving the bimodal kneading pair of the map has been derived. However, if the period of the critical points is large, long calculations are required to determine the Bowen-Franks group. Given two bimodal kneading pairs the *-product of these pairs was introduced in the paper of \textit{J.~P.~Lampreia}, \textit{R.~Severino} and \textit{J.~Sousa Ramos} [Grazer Math. Ber. 346, 245--254 (2004; Zbl 1061.37008)]. This product is again a bimodal kneading pair. The main result of the present paper provides a formula to calculate the Bowen-Franks group, if the kneading pair of the map can be written as the *-product of two kneading pairs.
reviewed by: Peter Raith
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 20K25
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 5016224
zbMATH Keywords: bimodal map
zbMATH Keywords: subshift of finite type
zbMATH Keywords: flow equivalence
zbMATH Keywords: Bowen-Franks group
zbMATH Keywords: kneading theory
MaRDI profile type: Publication
full work available at URL: j.laa.2005.09.011
OpenAlex ID: W2072147287
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DOI: 10.1016/J.LAA.2005.09.011
description: scientific article; zbMATH DE number 5016224