  The tomographic map of quantum state of a system with several degrees of
freedom which depends on one random variable, analogous to center of mass
considered in rotated and scaled reference frame in the phase space, is
constructed. Time evolution equation of the tomogram for this map is given in
explicit form. Properties of the map like the transition probabilities between
the different states and relation to the star product formalism are elucidated.
Example of multimode oscillator is considered in details. Symmetry properties
in respect to identical particles permutations are discussed in the framework
of proposed tomography scheme.
