关于Sofic S-间隙移位的计算
动力系统
2013-07-24 v5
摘要
设S={s_n}是N∪{0}的一个递增有限或无限子集，X(S)是与S相关的S-间隙移位。设f_S(x)=1-∑1/x^{s_n+1}为熵函数，该函数在2^{h(X(S))}处为零，其中h(X(S))是系统的熵。假设X(S)是sofic的，其邻接矩阵为A，特征多项式为χ_A。那么对于某个有理函数Q_S，有χ_A(x)=Q_S(x)f_S(x)。我们将显式确定这个Q_S。我们将证明，当|S|<∞或|S|=∞时，分别有ζ(t)=1/f_S(t^{-1})或ζ(t)=1/((1-t)f_S(t^{-1}))。这里ζ是X(S)的zeta函数。我们还将计算sofic S-间隙移位的Bowen-Franks群。
引用
@article{arxiv.1108.3414,
title = {Computations on Sofic S-gap Shifts},
author = {D. Ahmadi Dastjerdi and S. Jangjoo},
journal= {arXiv preprint arXiv:1108.3414},
year = {2013}
}
备注
This paper has been withdrawn due to extending results about SFT shifts to sofic shifts (Theorem 2.3). This forces to apply some minor changes in the organization of the paper. This paper has been withdrawn due to a flaw in the description of the adjacency matrix (2.3)