On topological entropy of transitive triangular maps

In the paper of Alsedà, Kolyada, Llibre and Snoha [L. Alsedà, S.F. Kolyada, J. Llibre, Lʹ. Snoha, Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc. 351 (1999) 1551–1573] there was—among others—proved that a nonminimal continuous transitive map f of a compact metric space ( X , ρ ) can be extended to a triangular map F on X × I (i.e., f is the base for F) in such a way that F is transitive and has the same entropy as f. The presented paper shows that under certain conditions the extension of minimal maps is guaranteed, too: Let ( X , f ) be a solenoidal dynamical system. Then there exist a transitive triangular map F such that h ( F ) = h ( f ) .