Square root of the monodromy map for the equation of RSJ model of Josephson junction

Several noteworthy properties of the differential equation utilized for the modeling of Josephson junctions are considered. The explicit representation of the monodromy transform of the space of its solutions is given. In case of positive integer order, the transformation interpreted as the square root of the monodromy transformation noted is derived making use of a symmetry the associated linear second order differential equation possesses.