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

Michael Schraudner. "A matrix formalism for conjugacies of higher-dimensional shifts of finite type." Colloquium Mathematicae 110.2 (2008): 493-515. <http://eudml.org/doc/283855>.

@article{MichaelSchraudner2008,
abstract = {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 ℤ⁺-matrices. Using the decomposition theorem every topological conjugacy between two $ℤ^\{d\}$-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.},
author = {Michael Schraudner},
journal = {Colloquium Mathematicae},
keywords = {state splittings; strong shift equivalence; matrix conditions; strictly essential presentations; algorithmic results},
language = {eng},
number = {2},
pages = {493-515},
title = {A matrix formalism for conjugacies of higher-dimensional shifts of finite type},
url = {http://eudml.org/doc/283855},
volume = {110},
year = {2008},
}

TY - JOUR
AU - Michael Schraudner
TI - A matrix formalism for conjugacies of higher-dimensional shifts of finite type
JO - Colloquium Mathematicae
PY - 2008
VL - 110
IS - 2
SP - 493
EP - 515
AB - 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 ℤ⁺-matrices. Using the decomposition theorem every topological conjugacy between two $ℤ^{d}$-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.
LA - eng
KW - state splittings; strong shift equivalence; matrix conditions; strictly essential presentations; algorithmic results
UR - http://eudml.org/doc/283855
ER -