  We introduce conservative curved systems over multiply connected domains and
study relationships of such systems with related notions of functional model,
characteristic function, and transfer function. In contrast to standard theory
for the unit disk, characteristic functions and transfer functions are
essentially different objects. We study possibility to recover the
characteristic function for a given transfer function. As the result we obtain
the procedure to construct the functional model for a given conservative curved
system. We employ the functional model to solve some problems in perturbation
theory.
