【講題】Transitivity and dense orbits for Markov tree-shifts

【演講時間】11月28日(星期五)下午1點30分  

【演講地點】清華大學校本部第二綜合大樓B側8樓A813室

【摘要】

This talk introduces Markov tree-shifts, a natural extension of classical Markov shifts to tree-structured symbolic systems. Unlike one-dimensional shifts, tree-shifts allow multiple branches to evolve in parallel, leading to richer dynamical behavior. We investigate topological transitivity and various notions of dense orbits, including ray dense and strong ray dense orbits, and characterize when these properties are equivalent. The results reveal when dynamical features of one-dimensional Markov shifts lift to the tree setting, and when genuinely new phenomena arise. This highlights the increased complexity and expressive power of symbolic dynamics on trees.