  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.
