论文标题
加权广义偏移的设置理论熵
Set-theoretical entropies of weighted generalized shifts
论文作者
论文摘要
在本文中，有限字段$ f $，一种非空的集合$γ$，一个自动映射$φ：γ\toγ$和flige vector $ \ mathfrak {w} \在f^γ$中，我们表明，套装的套件 - 加权的一般性shipt $ f^$σ_} $ c，f^w}的理论性熵或$+\ infty $，此外，当且仅当$σ_{φ，\ mathfrak {w}} $ is quasi - periodic时，它等于零。另一方面，在表征$σ_{φ，\ mathfrak {w}}}的所有条件之后：f^γ\ to f^γ$是有限纤维，我们表明，违反设置的违反设置 - 有限纤维的理论熵$ \ rm {supp}（\ mathfrak {w}）$。在最终部分中，我们研究了$σ_{φ，\ mathfrak {w}} $的限制到直接总和$ \ mathop {\ bigoplus} \limits_γf$。
In this paper for a finite field $F$, a nonempty set $Γ$, a self--map $φ:Γ\toΓ$ and a weight vector $\mathfrak{w}\in F^Γ$, we show that the set--theoretical entropy of the weighted generalized shift $σ_{φ,\mathfrak{w}}:F^Γ\to F^Γ$ is either zero or $+\infty$, moreover it is equal to zero if and only if $σ_{φ,\mathfrak{w}}$ is quasi--periodic. On the other hand after characterizing all conditions under which $σ_{φ,\mathfrak{w}}:F^Γ\to F^Γ$ is of finite fibre, we show that the contravariant set--theoretical entropy of a finite fibre $σ_{φ,\mathfrak{w}}:F^Γ\to F^Γ$ depends only on $φ$ and $\rm{supp}(\mathfrak{w})$. In final sections we study the restriction of $σ_{φ,\mathfrak{w}}$ to the direct sum $\mathop{\bigoplus}\limits_ΓF$.
