Jacobian elliptic Chebyshev rational maps

We introduce the Jacobian elliptic Chebyshev rational maps with the the equidistributivity property (or briefly EDP) and the semi-group property like the Chebyshev polynomial maps. Simple methods are also discussed for generating sequences of i.i.d. p-ary random variables based on the Jacobian elliptic Chebyshev rational maps. Furthermore, we give conjectures on correlational properties of a real-valued trajectory generated by the Jacobian elliptic Chebyshev rational maps.