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A class of invariants of the topological conjugacy of subshifts

Published online by Cambridge University Press:  09 August 2004

WOLFGANG KRIEGER
Affiliation:
Institute for Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany (e-mail: krieger@math.uni-heidelberg.de)
KENGO MATSUMOTO
Affiliation:
Department of Mathematical Sciences, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan (e-mail: kengo@yokohama-cu.ac.jp)

Abstract

The $\lambda$-entropy of a right-resolving $\lambda$-graph system is introduced as the upper asymptotic growth rate of the number of vertices at level n. It is shown that shift equivalent right-resolving $\lambda$-graph systems have the same $\lambda$-entropy. The $\lambda$-entropies of right-resolving $\lambda$-graph systems that are invariantly associated to subshifts are invariants of topological conjugacy. Finite directed graphs are used in the construction of compact forward separated Shannon graphs that have the structure of a pushdown automaton and that are invariantly associated to the subshift they present. To these compact forward separated Shannon graphs there correspond $\lambda$-graph systems whose $\lambda$-entropy is equal to the topological entropy of the edge shift of the finite directed graph. Examples are given.

Type
Research Article
Copyright
2004 Cambridge University Press

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