Algebraic shift equivalence and primitive matrices
M Boyle, D Handelman - Transactions of the American Mathematical …, 1993 - ams.org
Transactions of the American Mathematical Society, 1993•ams.org
Motivated by symbolic dynamics, we study the problem, given a unital subring $ S $ of the
reals, when is a matrix $ A $ algebraically shift equivalent over $ S $ to a primitive matrix?
We conjecture that simple necessary conditions on the nonzero spectrum of $ A $ are
sufficient, and establish the conjecture in many cases. If $ S $ is the integers, we give some
lower bounds on sizes of realizing primitive matrices. For Dedekind domains, we prove that
algebraic shift equivalence implies algebraic strong shift equivalence. References
reals, when is a matrix $ A $ algebraically shift equivalent over $ S $ to a primitive matrix?
We conjecture that simple necessary conditions on the nonzero spectrum of $ A $ are
sufficient, and establish the conjecture in many cases. If $ S $ is the integers, we give some
lower bounds on sizes of realizing primitive matrices. For Dedekind domains, we prove that
algebraic shift equivalence implies algebraic strong shift equivalence. References
Abstract
Motivated by symbolic dynamics, we study the problem, given a unital subring of the reals, when is a matrix algebraically shift equivalent over to a primitive matrix? We conjecture that simple necessary conditions on the nonzero spectrum of are sufficient, and establish the conjecture in many cases. If is the integers, we give some lower bounds on sizes of realizing primitive matrices. For Dedekind domains, we prove that algebraic shift equivalence implies algebraic strong shift equivalence. References
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