Monotone maps of 𝐺-like continua with positive topological entropy yield indecomposability

Abstract

In the previous paper Adv. Math. 304 (2017), pp. 793–808, we proved that if for any graph G G , a homeomorphism on a G G -like continuum X X has positive topological entropy, then the continuum X X contains an indecomposable subcontinuum. Also, if for a tree G G , a monotone map on a G G -like continuum X X has positive topological entropy, then the continuum X X contains an indecomposable subcontinuum. In this note, we extend these results. In fact, we prove that if for any graph G G , a monotone map on a G G -like continuum X X has positive topological entropy, then the continuum X X contains an indecomposable subcontinuum. Also we study topological entropy of monotone maps on Suslinean continua.