Topological entropy of diagonal maps on inverse limit spaces - Anušić, Ana; Mouron, Christopher (Topological Methods in Nonlinear Analysis, 2022)
We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space (I,f), where every diagonal component is the same map gI→ I which strongly commutes with f (i.e. f^-1° g=g° f^-1), we show that the entropy equals {Ent(f),Ent(g)}. As a side product, we develop some techniques for computing topological entropy of set-valued maps.