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The entropies of topological Markov shifts and a related class of algebraic integers

Published online by Cambridge University Press:  19 September 2008

D. A. Lind
D. A. Lind
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195, USA
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Abstract

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We give an algebraic characterization of the class of spectral radii of aperiodic non-negative integral matrices, and describe a method of constructing all such matrices with given spectral radius. The logarithms of the numbers in are the entropies of mixing topological Markov shifts. There is an arithmetic structure to , including factorization into irreducibles in only finitely many ways. This arithmetic structure has dynamical consequences, such as the impossibility of factoring the p-shift into a direct product of nontrivial homeomorphisms for prime p.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 283 - 300
Copyright
Copyright © Cambridge University Press 1984

References

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