Computations on Sofic S-gap Shifts

• D. Ahmadi Dastjerdi ^[1] ; S. Jangjoo
  1. [1] University of Guilan

     University of Guilan

     Irán

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 2, 2013, págs. 393-406
• Idioma: inglés
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• Resumen

  • Let S = {si ∈ N ∪ {0} : 0 ≤ si < si+1, i ∈ N} and X(S) the S-gap shift associated to S with entropy h(X(S)). Let fS(x) = 1 − 1 xsn+1 be the entropy function which will be vanished at 2h(X(S)). Suppose X(S) is sofic with adjacency matrix A and the characteristic polynomial χA. Then for some rational function QS, χA(x) = QS(x) fS(x). This QS will be explicitly determined. We will show that ζ (t) = 1 fS (t−1) or ζ (t) = 1 (1−t) fS (t−1) when |S| < ∞ or |S|=∞ respectively. Here ζ is the zeta function of X(S). We will also compute the Bowen–Franks groups of a sofic S-gap shift.