V.A. Rohlin asked in 1949 whether 2-fold mixing implies 3-fold mixing for a
stationary process indexed by Z, and the question remains open today. In 1978,
F. Ledrappier exhibited a counterexample to the 2-fold mixing implies 3-fold
mixing problem, the so-called "3-dot system", but in the context of stationary
random fields indexed by ZxZ. In this work, we first present an attempt to
adapt Ledrappier's construction to the one-dimensional case, which finally
leads to a stationary process which is 2-fold but not 3-fold mixing
conditionally to the sigma-algebra generated by some factor process. Then,
using arguments coming from the theory of joinings, we will give some strong
obstacles proving that Ledrappier's counterexample can not be fully adapted to
one-dimensional stationary processes