发表机构
Tianjin University（天津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究无叶局部有限根树上Cesàro空间加权后移算子的动力学，刻画其有界性、传递性、超循环性及混沌性，并给出反例说明各性质间关系。
AI 中文摘要
我们研究了与无叶局部有限根树相关的Cesàro空间上加权后移算子的动力学。首先，我们根据相邻层级基数和边权刻画了其有界性。然后，我们通过一个涉及层级基数、沿路径的权重乘积以及层级依赖的Cesàro因子的增长条件来刻画其$\mathcal{F}$-传递性。作为推论，我们获得了超循环性、弱混合、拓扑遍历性和拓扑混合的判据。我们还刻画了非零轨道极限点的存在性以及混沌加权移位，后者通过满足显式可和性条件的归一化不动点和单位流来刻画。例子表明，$\mathcal{F}_{\underline{d}>0}$-传递性不一定蕴含频繁超循环性，非超循环的加权移位仍可能具有非零轨道极限点，且拓扑混合不一定蕴含混沌。
英文摘要
We study the dynamics of weighted backward shifts on Ces`aro spaces associated with leafless locally finite rooted trees. We first characterize their boundedness in terms of adjacent level cardinalities and edge weights. We then characterize their $\mathcal{F}$-transitivity by a growth condition involving level cardinalities, products of weights along paths, and a level-dependent Ces`aro factor. As consequences, we obtain criteria for hypercyclicity, weak mixing, topological ergodicity, and topological mixing. We also characterize the existence of nonzero orbit limit points and chaotic weighted shifts, the latter in terms of normalized fixed points and unit flows satisfying an explicit summability condition. Examples show that $\mathcal{F}_{\underline{d}>0}$-transitivity need not imply frequent hypercyclicity, that a nonhypercyclic weighted shift may nevertheless have a nonzero orbit limit point, and that topological mixing need not imply chaos.
Comments22 pages, 1 figure
