Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?

Rune Johansen

doi:10.1007/978-3-642-39459-1_9

Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?

Department of Mathematical Sciences

Abstract

Is every irreducible shift of finite type flow equivalent to a renewal system? For the first time, this variation of a classic problem formulated by Adler is investigated, and several partial results are obtained in an attempt to find the range of the Bowen–Franks invariant over the set of renewal systems of finite type. In particular, it is shown that the Bowen–Franks group is cyclic for every member of a class of renewal systems known to attain all entropies realised by shifts of finite type, and several classes of renewal systems with non-trivial values of the invariant are constructed.

Original language	English
Title of host publication	Operator Algebra and Dynamics : Nordforsk Network Closing Conference, Faroe Islands, May 2012
Editors	Toke M. Clausen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov
Publisher	Springer
Publication date	2013
Pages	187-209
ISBN (Print)	9783642394584
ISBN (Electronic)	9783642394591
DOIs	https://doi.org/10.1007/978-3-642-39459-1_9
Publication status	Published - 2013

Series	Springer Proceedings in Mathematics & Statistics
Volume	58

Access to Document

10.1007/978-3-642-39459-1_9

http://link.springer.com/book/10.1007%2F978-3-642-39459-1

Cite this

Johansen, R. (2013). Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System? In T. M. Clausen, S. Eilers, G. Restorff, & S. Silvestrov (Eds.), Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012 (pp. 187-209). Springer. Springer Proceedings in Mathematics & Statistics Vol. 58 https://doi.org/10.1007/978-3-642-39459-1_9

Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System? / Johansen, Rune.

Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. ed. / Toke M. Clausen; Søren Eilers; Gunnar Restorff; Sergei Silvestrov. Springer, 2013. p. 187-209 (Springer Proceedings in Mathematics & Statistics , Vol. 58).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Johansen, R 2013, Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System? in TM Clausen, S Eilers, G Restorff & S Silvestrov (eds), Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. Springer, Springer Proceedings in Mathematics & Statistics , vol. 58, pp. 187-209. https://doi.org/10.1007/978-3-642-39459-1_9

@inproceedings{f4e0b4fba9eb46dba7330b6fbab65dcd,

title = "Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?",

abstract = "Is every irreducible shift of finite type flow equivalent to a renewal system? For the first time, this variation of a classic problem formulated by Adler is investigated, and several partial results are obtained in an attempt to find the range of the Bowen–Franks invariant over the set of renewal systems of finite type. In particular, it is shown that the Bowen–Franks group is cyclic for every member of a class of renewal systems known to attain all entropies realised by shifts of finite type, and several classes of renewal systems with non-trivial values of the invariant are constructed.",

author = "Rune Johansen",

year = "2013",

doi = "10.1007/978-3-642-39459-1_9",

language = "English",

isbn = "9783642394584",

series = "Springer Proceedings in Mathematics & Statistics ",

pages = "187--209",

editor = "Clausen, {Toke M.} and Eilers, {S{\o}ren } and Restorff, {Gunnar } and Silvestrov, {Sergei }",