Shift equivalence, by M. Michael Boyle

Topology Atlas Document # zaaa-54.htm | Production Editor: R. Flagg

Topology Atlas Invited Contributions, vol. 1, issue 3 (1996), 30.

Shift equivalence
by

M. Michael Boyle

(University of Maryland, College Park, MD 20742-0001, U.S.A.)

Shift equivalence is an equivalence relation introduced by R.F. Williams in an attempt to classify shifts of finite type up to topological conjugacy. For many references and an indication of the problems and results involving shift equivalence, consult my survey article "Symbolic dynamics and matrices", pp. 1-38 in the book Combinatorial and Graph-Theoretical Problems in Linear Algebra (1993), Vol. 50 of IMA Volumes in Mathematics and its Applications, eds. R. Brualdi, S. Friedland and V. Klee. That article is an introduction to shifts of finite type and associated matrix problems and results. The table of contents of the article is below.

Contents

Introduction
Shifts of finite type
Matrix invariants
Shift equivalence, strong shift equivalence
Zeta functions and spectra
Graphs via polynomial matrices
More Williams' problems
General matrices
Inverse problems and the submatrix theorem
One-sided subshifts
Quotients
References

Received by the editors: December 22, 1995.