学术报告报告题目：Entropyof 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 oftree shifts of finite type with and without boundary conditions. Wedemonstrate that computing the entropy of a tree shift of finite typeis equivalent to solving a system of nonlinear recurrence equations.Furthermore, the entropy of binary Markov tree shifts defined on twosymbols is either 0 or ln 2. Meanwhile, the realization of entropy ofone-dimensional shifts of finite type is elaborated, which indicatesthat tree shifts are capable of rich phenomena. Considering theinfluence of three different types of boundary conditions, say, theperiodic, Dirichlet, and Neumann boundary conditions, the necessaryand sufficient condition for the coincidence of entropy with andwithout boundary condition are addressed.
报告题目：Topologicalaspects 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 aschaos, irreducibility, and mixing, of a one-sided shift of finitetype is well elucidated. Meanwhile, the investigation ofmultidimensional shifts, for instance, the textile systems, isdifficult and only a few results have been obtained so far.
In this talk, we consider shiftsdefined on infinite trees, that are called tree-shifts. Infinitetrees have a natural structure of one-sided symbolic dynamicalsystems equipped with multiple shift maps and constitute anintermediate class in between one-sided shifts and multidimensionalshifts. We have shown that, not only an irreducible tree-shift offinite type, but a mixing tree-shift are chaotic in the sense ofDevaney. Furthermore, the graph and labeled graph representations oftree-shifts are revealed so that the verification of irreducibilityand mixing of a tree-shift is equivalent to determining theirreducibility and mixing of matrices, respectively. This extends theclassical results of one-sided symbolic dynamics.
A necessary and sufficientcondition for the irreducibility and mixing of tree-shifts of finitetype is demonstrated. Most important of all, the examination can bedone in finite steps with an upper bound.
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数学学院
2015年9月8日