Anisotropic properties of longitudinally inhomogeneous medium with linear birefringence and dichroism were considered. Differential Jones matrix model for this class of media was obtained. The equation for the polarization complex variable that describes the evolution of polarization state in this class of media was found. Partial solutions describing evolution of the privileged polarization states were obtained. The features of privileged polarization states and the conditions of their existence in this class of media were analyzed.

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