论文标题
跨性别系统中的家庭敏感性破裂
Broken family sensitivity in transitive systems
论文作者
论文摘要
令$（x，t）$为拓扑动力系统，$ n \ geq 2 $和$ \ mathcal {f} $是$ \ mathbb {z} _+$的子集的Furstenberg家族。 $（x，t）$称为损坏$ \ MATHCAL {f} $ - $ n $ sentive，如果存在$δ> 0 $和$ f \ in \ Mathcal {f} $，以至于每个opene（non-oppent opent opent opent opent opent）subset $ u $ $ x $ of $ x $ of $ x $，并且每个$ l \ in \ inthbb in \ mathbb { $ x_1^l，x_2^l，\ dotsc，x_n^l \ in u $和$ m_l \ in \ mathbb {z} _+ $满足$ d（t^k x_i^l，t^k x_i^l，t^k x_j^l）>Δ我们调查了所有分段辛迪克子集的家庭（$ \ Mathcal {f} _ {ps} $）的破碎$ \ Mathcal {f} $ - $ n $ - sensitivity，这是所有积极的上层Banach密度子集的家族（$ \ Mathcal {f} _ {f} _ {pubd} $） （$ \ mathcal {f} _ {inf} $）。我们表明，传递系统$（x，t）$被打破$ \ nathcal {f} $ - $ n $ - 对$ \ Mathcal {f} = \ Mathcal {f} _ {f} _ {ps} \ \ \ \ \ \ \ \ \ \\ text {or} or} \ \ \ \ \ \ \ \ \ \ nisive in Is Insive in Is Incielist if-ifist if-ifist if-ifist if-ifist if-ifist $（x^n，t^{（n）}）$的$ \ MATHCAL {F} $ - 循环点; $ \ nathcal {f} _ {inf} $ - $ n $ - 敏感时，只有存在必需的$ n $ n $ sentive tuple $（x_1，x_1，x_2，\ dotsc，x_n）$ n} d（t^kx_i，t^kx_j）> 0 $。我们还通过分析其最大等效因素的因子图来获得它们的特定特性。此外，我们展示了区分不同种类破碎的家庭敏感性的例子。
Let $(X,T)$ be a topological dynamical system, $n\geq 2$ and $\mathcal{F}$ be a Furstenberg family of subsets of $\mathbb{Z}_+$. $(X,T)$ is called broken $\mathcal{F}$-$n$-sensitive if there exist $δ>0$ and $F\in\mathcal{F}$ such that for every opene (non-empty open) subset $U$ of $X$ and every $l\in\mathbb{N}$, there exist $x_1^l,x_2^l,\dotsc,x_n^l\in U$ and $m_l\in \mathbb{Z}_+$ satisfying $d(T^k x_i^l, T^k x_j^l)> δ,\ \forall 1\leq i<j\leq n, k\in m_l+ F\cap[1,l]$. We investigate broken $\mathcal{F}$-$n$-sensitivity for the family of all piecewise syndetic subsets ($\mathcal{F}_{ps}$), the family of all positive upper Banach density subsets ($\mathcal{F}_{pubd}$) and the family of all infinite subsets ($\mathcal{F}_{inf}$). We show that a transitive system $(X,T)$ is broken $\mathcal{F}$-$n$-sensitive for $\mathcal{F}=\mathcal{F}_{ps}\ \text{or}\ \mathcal{F}_{pubd}$ if and only if there exists an essential $n$-sensitive tuple which is an $\mathcal{F}$-recurrent point of $(X^n, T^{(n)})$; is broken $\mathcal{F}_{inf}$-$n$-sensitive if and only if there exists an essential $n$-sensitive tuple $(x_1,x_2,\dotsc,x_n)$ such that $\limsup_{k\to\infty}\min_{1\leq i<j\leq n}d(T^kx_i,T^kx_j)>0$. We also obtain specific properties for them by analyzing the factor maps to their maximal equicontinuous factors. Furthermore, we show examples to distinguish different kinds of broken family sensitivity.
