#### 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.

#### 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.

https://works.swarthmore.edu/fac-math-stat/67

## Comments

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