学术报告 报告题目：Entropy of tree shifts of finite type
报 告 人：班荣超教授（台湾东华大学）
报告时间：9月10日（周四）下午15:00—16:00
报告地点：4号楼4318室
报告摘要：
This talk studies the entropy of tree shifts of finite type with and without boundary conditions. We demonstrate that computing the entropy of a tree shift of finite type is equivalent to solving a system of nonlinear recurrence equations. Furthermore, the entropy of binary Markov tree shifts defined on two symbols is either 0 or ln 2. Meanwhile, the realization of entropy of one-dimensional shifts of finite type is elaborated, which indicates that tree shifts are capable of rich phenomena. Considering the influence of three different types of boundary conditions, say, the periodic, Dirichlet, and Neumann boundary conditions, the necessary and sufficient condition for the coincidence of entropy with and without boundary condition are addressed.
报告题目：Topological aspects of tree-shifts
报 告 人：张志鸿教授（台湾高雄大学）
报告时间：9月10日（周四）下午16:15—17:15
报告地点：4号楼4318室
报告摘要：
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. Infinite 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-shift 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.
欢迎广大师生前往!
数学学院
2015年9月8日