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December 2008 $AH$-substitution and Markov Partition of a Group Automorphism on $T^d$
Fumihiko ENOMOTO
Tokyo J. Math. 31(2): 375-398 (December 2008). DOI: 10.3836/tjm/1233844059


The existence of a Markov partition of a hyperbolic group automorphism generated by an integral matrix with determinant $\pm 1$ is established by Sinai (see [22]). After that, there are many articles to construct Markov partitions of group automorphisms generated by non-negative matrices satisfying Pisot condition by the tiling method from substitutions (see [1], [7], [16], [19], [5]). One of the purpose of this paper is to establish the construction method of a Markov partition for a group automorphism generated by a non-positive matrix satisfying ``negative Pisot'' condition. An anti-homomorphic extension of a substitution, called $AH$-substitution, is introduced in the paper. Owing to this new substitution, the Markov partition of the group automorphism from the non-positive integral matrix is constructed.


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Fumihiko ENOMOTO. "$AH$-substitution and Markov Partition of a Group Automorphism on $T^d$." Tokyo J. Math. 31 (2) 375 - 398, December 2008.


Published: December 2008
First available in Project Euclid: 5 February 2009

zbMATH: 1177.37012
MathSciNet: MR2477879
Digital Object Identifier: 10.3836/tjm/1233844059

Rights: Copyright © 2008 Publication Committee for the Tokyo Journal of Mathematics


Vol.31 • No. 2 • December 2008
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