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

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Operator Algebra and Dynamics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 58))

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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.

Mathematics Subject Classification (2010): 37B10.

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Acknowledgements

Supported by VILLUM FONDEN through the experimental mathematics network at the University of Copenhagen. Supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92).

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark

    Rune Johansen

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  1. Rune Johansen
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Correspondence to Rune Johansen .

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Editors and Affiliations

  1. Dept. of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Toke M. Carlsen

  2. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Søren Eilers

  3. Dept. of Science and Technology, University of the Faroe Islands, Tórshavn, Faroe Islands

    Gunnar Restorff

  4. Culture and Communication (UKK) Division of Applied Mathematics The School of Education, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

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Johansen, R. (2013). Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?. In: Carlsen, T., Eilers, S., Restorff, G., Silvestrov, S. (eds) Operator Algebra and Dynamics. Springer Proceedings in Mathematics & Statistics, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39459-1_9

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