Rates of Recurrence Z(sup q) and R(sup q) Extensions of Subshifts of Finite Type

摘要

In the note the authors give new asymptotic formulae for certain countingfunctions associated to the periodic behavior of Z(sup q) and R(sup q) extensions of subshifts of finite type. In the case of the Z(sup q) extensions, these strengthen previous estimates of Marcus and Tuncel. For both types of extension, their results complement the central limit type results of Lalley. Their proof requires the application of ideas from thermodynamic formalism. While developing this approach, in section 2, they take the opportunity to present a counter example to a related conjecture of Coelho.