Application of Infinite Labeled Graphs to Symbolic Dynamical Systems

Kengo Matsumoto ()
Additional contact information
Kengo Matsumoto: Joetsu University of Education, Department of Mathematics

Chapter Chapter 6 in Structural Analysis of Complex Networks, 2011, pp 137-168 from Springer

Abstract: Abstract We apply a theory of infinite labeled graphs to studying presentations and classifications of symbolic dynamical systems, by introducing a class of infinite labeled graphs, called λ-graph systems. Its matrix presentation is called a symbolic matrix system. The notions of a λ-graph system and symbolic matrix system are generalized notions of a finite labeled graph and symbolic matrix for sofic subshifts to general subshifts. Strong shift equivalence and shift equivalence between symbolic matrix systems are formulated so that two subshifts are topologically conjugate if and only if the associated canonical symbolic matrix systems are strong shift equivalent. We construct several kinds of shift equivalence invariants for symbolic matrix systems. They are the dimension groups, the K-groups, and the Bowen–Franks groups that are generalizations of the corresponding notions for nonnegative matrices. They yield topological conjugacy invariants of subshifts. The entropic quantities called λ-entropy and volume entropy for λ-graph systems are also studied related to the topological entropy of symbolic dynamics.

Keywords: Subshifts; Symbolic dynamics; λ-Graph systems; Strong shift equivalence; Bowen–Franks group; K-theory; Topological entropy (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4789-6_6

Ordering information: This item can be ordered from
http://www.springer.com/9780817647896

DOI: 10.1007/978-0-8176-4789-6_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().