a triangular map of type 2∞ with positive topological entropy on a minimal set

we provide a class of triangular maps of the square, (x,y)↦(f(x),g_x(y)) of type 2^∞, i.e., such that the periods of periodic points are the powers of 2, which has a minimal set supporting positive topological entropy. this improves the famous example by s. kolyada from 1992 and contributes to the solution of an old problem by a.n. sharkovsky.