  We study the problem of detecting the structure of a complex dynamical system
described by a set of deterministic differential equation that contains a
Hamiltonian subsystem, without any information on the explicit form of
evolution laws. We suppose that initial conditions are random and the initial
conditions of the Hamiltonian subsystem are independent from the initial
conditions of the rest of the system. The single numerical information is the
probability density function of the system at one or several, finite number of
time instants. In the framework of the formalism of the generalized R\'{e}nyi
entropy we find necessary and sufficient conditions that the back reaction of
the Hamiltonian subsystem to the rest of the system is negligible.The results
can be easily generalized to the case of general, measure preserving subsystem.
