Balanced strong shift equivalence, balanced in-splits, and eventual conjugacy

Authors

Kevin Aguyar Brix, University of Wollongong

Publication Name

Ergodic Theory and Dynamical Systems

Abstract

We introduce the notion of balanced strong shift equivalence between square non-negative integer matrices, and show that two finite graphs with no sinks are one-sided eventually conjugate if and only if their adjacency matrices are conjugate to balanced strong shift equivalent matrices. Moreover, we show that such graphs are eventually conjugate if and only if one can be reached by the other via a sequence of out-splits and balanced in-splits, the latter move being a variation of the classical in-split move introduced by Williams in his study of shifts of finite type. We also relate one-sided eventual conjugacies to certain block maps on the finite paths of the graphs. These characterizations emphasize that eventual conjugacy is the one-sided analog of two-sided conjugacy.

Open Access Status

This publication may be available as open access

Volume

42

Issue

1

First Page

19

Last Page

39