Rates of Recurrence for Zq and Rq Extensions of Subshifts of Finite Type
Rates of Recurrence for Zq and Rq Extensions of Subshifts of Finite Type
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DOI：
10.1112/jlms/49.2.401
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发表时间：
1994-04
影响因子：
1.2
通讯作者：
M. Pollicott;Richard Sharp
中科院分区：
文献类型：
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作者：
M. Pollicott;Richard Sharp
在这篇注记中，我们给出了与有限型子移位的Zq和Rq的周期行为有关的某些计数函数的新的渐近公式。在Zq扩张的情况下，这些加强了先前对Marcus和Tuncel的估计[9]。对于这两种类型的扩张，我们的结果补充了Lley[6]的中心极限类型的结果。我们的证明需要应用热力学形式主义的思想。在发展这种方法的同时，在第2节中，我们借此机会对Coelho-Filho的一个相关猜想提出一个反例[2]。
In this note we give new asymptotic formulae for certain counting functions associated to the periodic behaviour of Zqand Rqextensions of subshifts of finite type. In the case of the Zqextensions, these strengthen previous estimates of Marcus and Tuncel [9]. For both types of extension, our results complement the central limit type results of Lalley [6]. Our proof requires the application of ideas from thermodynamic formalism. Whilst developing this approach, in Section 2, we take the opportunity to present a counter‐example to a related conjecture of Coelho‐Filho [2].