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Induced dynamics is defined as dynamics of real zeros with respect to $x$ of equation $f(q_1-x,\ldots,q_N-x,p_1,\ldots,p_N)=0$, where $f$ is a function, and $q_i$ and $p_j$ are canonical variables obeying some (free) evolution. Identifying zero level lines with the world lines of particles, we show that the resulting dynamical system demonstrates highly nontrivial collisions of particles. In particular, induced dynamical systems can describe such ``quantum'' effects as bound states and creation/annihilation of particles, both in nonrelativistic and relativistic cases. On the other side, induced dynamical systems inherit properties of the $(p,q)$-systems being Hamiltonian and Liouville integrable., Comment: LaTeX, 15 pages, 12 figures

We study(h)-minimal configurations in Aubry-Mather theory, wherehbelongs to a complete metric space of functions. Such minimal configurations have definite rotation number. We establish the existence of a set of functions, which is a countable intersection of open everywhere dense subsets of the space and such that for each elementhof this set and each rational numberα, the following properties hold: (i) there exist three different(h)-minimal configurations with rotation numberα; (ii) any(h)-minimal configuration with rotation numberαis a translation of one of these configurations.