  In describing a dynamical system, the greatest part of the work for a
theoretician is to translate experimental data into differential equations. It
is desirable for such differential equations to admit a Lagrangian and/or an
Hamiltonian description because of the Noether theorem and because they are the
starting point for the quantization. As a matter of fact many ambiguities arise
in each step of such a reconstruction which must be solved by the ingenuity of
the theoretician. In the present work we describe geometric structures emerging
in Lagrangian, Hamiltonian and Quantum description of a dynamical system
underlining how many of them are not really fixed only by the trajectories
observed by the experimentalist.
