论文标题
关于结构定理和非饱和示例
On structure theorems and non-saturated examples
论文作者
论文摘要
对于任何最小系统$（x，t）$和$ d \ geq 1 $，都有一个关联的最小系统$（n_ {d}（x），\ Mathcal {g} _ {d}（t））$，其中$ \ Mathcal {G} _ {g} _ {d} _ {d} _ {d}（t）$是$ time $ time $ time time $ t time time time $ t \ cd。 t^2 \ times \ cdots \ times t^{d} $和$ n_ {d}（x）$是$ \ Mathcal {g} _ {d}（t）$下对角线的孔闭合。众所周知，$ n_d（x）$的最大$ d $ d $ d $ step pro-nilfactor是$ n_d（x_d）$，其中$ x_d $是$ x $的最大$ d $ d $ d $ d $ - 步骤pro-nilfactor。 在本文中，我们进一步研究了$ n_d（x）$的结构。我们表明，$ n_d（x）$的最大远端因子是$ n_d（x_ {dis}）$，$ x_ {dis} $是$ x $的最大远端因子，并证明是最小的systems $（n_ {d}（d}（d}（x）（x），x），\ nathcal {g nathcal {g} g} $ sature n n $此外，构建了一个非饱和度量示例$（x，t）$，不是$ t \ times t^2 $饱和，是一个toeplitz的最小系统。
For any minimal system $(X,T)$ and $d\geq 1$ there is an associated minimal system $(N_{d}(X), \mathcal{G}_{d}(T))$, where $\mathcal{G}_{d}(T)$ is the group generated by $T\times\cdots\times T$ and $T\times T^2\times\cdots\times T^{d}$ and $N_{d}(X)$ is the orbit closure of the diagonal under $\mathcal{G}_{d}(T)$. It is known that the maximal $d$-step pro-nilfactor of $N_d(X)$ is $N_d(X_d)$, where $X_d$ is the maximal $d$-step pro-nilfactor of $X$. In this paper, we further study the structure of $N_d(X)$. We show that the maximal distal factor of $N_d(X)$ is $N_d(X_{dis})$ with $X_{dis}$ being the maximal distal factor of $X$, and prove that as minimal systems $(N_{d}(X), \mathcal{G}_{d}(T))$ has the same structure theorem as $(X,T)$. In addition, a non-saturated metric example $(X,T)$ is constructed, which is not $T\times T^2$-saturated and is a Toeplitz minimal system.
