is point the JMT circuit multiplies the vector X = (51/52/53/54) by Rki obtaining an estimate of the position of the reference point These estimates are averaged in the time Tu to eliminate almost completely the effect of the ASE noise and of the modulation. An average estimate of the positions of the reference vectors IIk is thus obtained. This estimate, that we call (RX)k. depends on the differential rotation happened in the preceding updated interval during fiber propagation. At this point, the inverse Jones matrix update, which coincides with the differential rota- tion of the quadrature space, can be obtained solving the following linear system: <RX)1 (9.39) (RX)3 where AM+ is a unitary 4 X 4 real matrix 0 is the 4 X 4 null matrix (RX)k and II are four components vector in the quadrature space. System (9.39) is generally largely redundant, since only three out of the 16 parameters of the matrix AM+ are independent variables, but it is necessary to consider three reference points (and not only two as indicated in [56]) to manage the degenerate case of a four Next Generation Transmission Systems dimensional rotation that leaves the plane containing two reference points unchanged in the quadrature space. This particular case arises from the fact that differential rotations in a four dimensional space cannot be described as rotations around an axis, as it happens in the three dimen- sional case. Rotation around an axis is an idea fostered by our experience, but it is only a coincidence that any rotation in three-space can be determined by an axis in three-space. For example, let us consider the idea of rotation in a two dimensional space. The "rota- tion axis" seems perpendicular to the space where the rotation happens: it is not even contained in it, and we can think about it only because we continuously image our plane immerged in a three dimensional space. Rotations, whatever the space dimensionality is, are more properly thought as parallel to a plane. This way of thinking is consistent with two dimensions (