The Decomposition Theorem For Two-Dimensional Shifts Of Finite Type

Authors

Aimee S. A. Johnson, Swarthmore CollegeFollow
K. M. Madden

Document Type

Article

Publication Date

5-1-1999

Published In

Proceedings Of The American Mathematical Society

Abstract

A one-dimensional shift of finite type can be described as the collection of bi-infinite "walks" along an edge graph. The Decomposition Theorem states that every conjugacy between two shifts of finite type can be broken down into a finite sequence of splittings and amalgamations of their edge graphs. When dealing with two-dimensional shifts of finite type, the appropriate edge graph description is not as clear; we turn to Nasu's notion of a "textile system" for such a description and show that all two-dimensional shifts of finite type can be so described. We then define textile splittings and amalgamations and prove that every conjugacy between two-dimensional shifts of finite type can be broken down into a finite sequence of textile splittings, textile amalgamations, and a third operation called an inversion.

Comments

This work is freely available courtesy of the American Mathematical Society.

Recommended Citation

Aimee S. A. Johnson and K. M. Madden. (1999). "The Decomposition Theorem For Two-Dimensional Shifts Of Finite Type". Proceedings Of The American Mathematical Society. Volume 127, Issue 5. 1533-1543. DOI: 10.1090/S0002-9939-99-04678-X
https://works.swarthmore.edu/fac-math-stat/67