发表机构
School of Mathematics, Tianjin University; School of Mathematics and Statistics, Henan Normal University（天津大学数学学院; 河南师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究了有向格图上后向平移的$\mathcal F$-传递性，给出了有限宽度格的精确权重刻画及无限象限格的等价条件，部分解决了相关开放问题。
AI 中文摘要
我们研究了有限宽度和无限宽度的有向格图上后向平移的$\mathcal F$-传递性。对于加权$\ell^p$-或$c_0$-空间上的单侧和双侧有限宽度格，我们获得了任意Furstenberg族$\mathcal F$的$\mathcal F$-和$\widetilde{\mathcal F}$-传递性的精确权重刻画。若$\mathcal F$是有限不变的，这些条件也刻画了拓扑$\mathcal F$-回复性。对于加权$\ell^2$-空间上具有径向权重的无限象限格，通过有限维约化和Pascal型转移矩阵的尖锐最小奇异值估计，我们得到了$\mathcal F$-传递性、超循环性和混合性的等价刻画。这为Baranov、Lishanskii和Papathanasiou提出的关于无限格图上超循环性的开放问题，在径向$\ell^2$情形下提供了部分解答。临界指数增长率下的例子说明了我们的准则所提供的更精细的动力信息。
英文摘要
We study $\mathcal F$-transitivity of backward shifts on finite- and infinite-width directed lattice graphs. For the unilateral and bilateral finite-width lattices on weighted $\ell^p$- or $c_0$-spaces, we obtain exact weight characterizations of $\mathcal F$- and $\widetilde{\mathcal F}$-transitivity for an arbitrary Furstenberg family $\mathcal F$. If $\mathcal F$ is finitely invariant, these conditions also characterize topological $\mathcal F$-recurrence. For the infinite quadrant lattice with radial weights on weighted $\ell^2$-spaces, a finite-dimensional reduction and sharp smallest-singular-value estimates for Pascal-type transfer matrices yield equivalent characterizations of $\mathcal F$-transitivity, hypercyclicity and mixing. This provides a partial answer, in the radial $\ell^2$-setting, to the open problem posed by Baranov, Lishanskii and Papathanasiou concerning hypercyclicity on the infinite lattice graph. Examples at the critical exponential growth rate illustrate the finer dynamical information provided by our criteria.
Comments29 pages, 3 figures
