Abstract:

In this talk, we will discuss the multiplicative integer systems on trees, those are countable graphs with no loop, and compute their entropies, which are usually used to measure the complexity of them. This talk is divided into two parts. In part I, we first introduce the q-multiplicative subshift on trees (q-MST) and present an explicit formula for the entropy of q-MST. Also, the coupled q-MST is considered, which is the intersection of a q-MST and a tree subshift. In a particular class, we provide a lower bound of the entropy of the coupled q-MST by using the entropy of its associated tree subshift. In part II, we study the multiple multiplicative subshift on trees (MMST). When the subshift is a one-step subshift of finite type, the explicit entropy formula can be obtained under certain conditions.