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

We provide a class of triangular maps of the square, (x,y)↦(f(x),gx(y))(x,y)↦(f(x),gx(y)) of type 2∞2∞, i.e., such that the periods of periodic points are the powers of 22, 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.