Title. TOPOLOGICAL ASPECTS OF TREE-SHIFTS

Abstract.The topological behavior, such as chaos, irreducibility, and mixing, of a one-sided shift of finite type is well elucidated. Meanwhile,

the investigation of multidimensional shifts, for instance, the textile systems, is difficult and only a few results have been obtained so far. In this talk, we consider shifts defined on infinite trees, that are called tree-shifts. In finite trees have a natural structure of one-sided symbolic dynamical systems equipped with multiple shift maps and constitute an intermediate class in between one-sided shifts and multidimensional shifts. We have shown that, not only an irreducible tree-shift of finite type, but a mixing tree-shifts are chaotic in the sense of Devaney. Furthermore, the graph and labeled graph representations of tree-shifts are revealed so that the verification of irreducibility and mixing of a tree-shift is equivalent to determining the irreducibility and mixing of matrices, respectively. This extends the classical results of one-sided symbolic dynamics. A necessary and sufficient condition for the irreducibility and mixing of tree-shifts of finite type is demonstrated. Most important of all, the examination can be done in finite steps with an upper bound.

报 告 人：张志鸿博士台湾国立高雄大学

报告时间：2015年9月7日（星期一）下午4：00

报告地点：数学科学学院38号楼报告厅

主办单位：数学科学学院

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