3-dimensional i.i.d. binary random vectors governed by Jacobian elliptic space curve dynamics

摘要

Sufficient conditions have been recently given for a classs of ergodic maps of an interval onto itself: I = [0, 1]∩R→I and its associated bi-nary function to generate a sequence of independent and identically dis-tributed (i.i.d.) binary random variables. Jacobian elliptic Chebyshev map, its derivative and second derivative induce Jacobian elliptic space curve. A mapping of the space curve with its coordinates, e.g., X, Y and Z, onto itself is introduced which defines 3 projective onto mappings, represented in the form of rational functions of {x_n, y_n, z_n}_(n=0)~∞. Such mappings with their absolutely continuous invariant measures as functions of elliptic integrals and their associated binary function can generate a 3-dimensional sequence of i.i.d. binary random vectors.