A matrix formalism for conjugacies of higher-dimensional shifts of finite type

Michael Schraudner¹

¹ Centro de Modelamiento Matemático Universidad de Chile (CNRS UMI 2807) Av. Blanco Encalada 2120 Santiago de Chile, Chile

Colloquium Mathematicum, Tome 110 (2008) no. 2, pp. 493-515.

Résumé

We develop a natural matrix formalism for state splittings and amalgamations of higher-dimensional subshifts of finite type which extends the common notion of strong shift equivalence of ${\mathbb Z}^+$-matrices. Using the decomposition theorem every topological conjugacy between two ${\mathbb Z}^d$-shifts of finite type can thus be factorized into a finite chain of matrix transformations acting on the transition matrices of the two subshifts. Our results may be used algorithmically in computer explorations on topological conjugacies and in the search for new conjugacy invariants.

Détail

DOI : 10.4064/cm110-2-12

Keywords: develop natural matrix formalism state splittings amalgamations higher dimensional subshifts finite type which extends common notion strong shift equivalence mathbb matrices using decomposition theorem every topological conjugacy between mathbb d shifts finite type factorized finite chain matrix transformations acting transition matrices subshifts results may algorithmically computer explorations topological conjugacies search conjugacy invariants