國立清華大學 數學系

Abstract: 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 ináuence of thre different types of boundary conditions, say, the periodic, Dirichlet, and Neumann boundary conditions, the necessary and su¢ cient condition for the coincidence of entropy with and without boundary condition are addressed. Tea Time: 3:00PM, R707