Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has
established strong connections with many areas, including linear algebra, graph theory …

Let σ=(λ1,…, λn) be a list of complex numbers. The nonnegative inverse eigenvalue problem
(NIEP) is the problem of determining necessary and sufficient conditions in order that σ be …

Classification of SFTs and the Little Shift Equivalence Conjecture Range of the dimension
representation Positive Rational Shift Equivalence Conjecture The Generalized Spectral …

We show that there exist real numbers $\lambda _1,\lambda _2,\dotsc,\lambda _n $ that
occur as the eigenvalues of an entry-wise nonnegative $ n $-by-$ n $ matrix but do not occur …

We study self-homeomorphisms of zero dimensional metrizable compact Hausdorff spaces
by means of the ordered first cohomology group, particularly in the light of the recent work of …

The Williams Conjecture is False for Irreducible Subshifts Page 1 Annals of Mathematics, 149
(1999), 545-558 The Williams Conjecture is false for irreducible subshifts By KH KIM and FW …

We characterize the possible nonzero spectra of primitive integer matrices (the integer case
of Boyle and Handelman's Spectral Conjecture). Characterizations of nonzero spectra of …

This paper discusses strong shift equivalence and counterexamples to the long standing
Shift Equivalence Problem in symbolic dynamics. We also discuss how strong shift …

Introduction. The main purpose of this article is to give some overview of matrix problems
and results in symbolic dynamics. The basic connection is that a nonnegative integral matrix …

Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by
discretizing space as well as time. The development of information theory gave impetus to …