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Constant-to-one and onto global maps of homomorphisms between strongly connected graphs

Published online by Cambridge University Press:  19 September 2008

Masakazu Nasu
Masakazu Nasu
Affiliation:
Faculty of Engineering, Mie University, Tsu 514, Japan
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Abstract

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The global maps of homomorphisms of directed graphs are very closely related to homomorphisms of a class of symbolic dynamical systems called subshifts of finite type. In this paper, we introduce the concepts of ‘induced regular homomorphism’ and ‘induced backward regular homomorphism’ which are associated with every homomorphism between strongly connected graphs whose global map is finite-to-one and onto, and using them we study the structure of constant-to-one and onto global maps of homorphisms between strongly connected graphs and that of constant-to-one and onto homomorphisms of irreducible subshifts of finite type. We determine constructively, up to topological conjugacy, the subshifts of finite type which are constant-to-one extensions of a given irreducible subshift of finite type. We give an invariant for constant-to-one and onto homomorphisms of irreducible subshifts of finite type.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 3 , September 1983 , pp. 387 - 413
Copyright
Copyright © Cambridge University Press 1983

References

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