On topological entropy of commuting tree maps Original Research Article

Let TT be a tree with ss ends and f,gf,g be continuous maps from TT to TT with f∘g=g∘ff∘g=g∘f. In this note we show that if there exists a positive integer m≥2m≥2 such that gcd(m,l)=1gcd(m,l)=1 for any 2≤l≤s2≤l≤s and f,gf,g share a periodic point which is a kmkm-periodic point of ff for some positive integer kk, then the topological entropy of f∘gf∘g is positive.