ncts

In this talk, I will discuss the monotonicity of topological entropy and topological pressure on tree-shifts, which are proposed by Petersen and Salama in their recent works. As is observed previously in the literature, the topological entropy of golden-mean shifts over rooted $d$ -trees is strictly increasing in $d$ . I would like to demonstrate how we extend this non-decreasing property to isotropic axial products of one-sided Markov subshifts, including golden-mean shifts. In particular, I will outline how a standard argument in the large deviation theory can be effectively applied to the combinatorial problem of interest. Applications of our result to shift spaces over several different underlying structures will also be briefed in the end of the talk. This is a joint work with Jung-Chao Ban.