  Describing the phenomena of the surrounding world is an interesting task that
has long attracted the attention of scientists. However, even in seemingly
simple phenomena, complex dynamics can be revealed. In particular, leaves on
the surface of various bodies of water exhibit complex behavior. This paper
addresses an idealized description of the mentioned phenomenon. Namely, the
problem of the plane-parallel motion of an unbalanced circular disk moving in a
stream of simple structure created by a point source is considered. Note that
using point sources, it is possible to approximately simulate the work of
skimmers used for cleaning swimming pools. Equations of joint motion of the
unbalanced circular disk and the point source. It is shown that in the case of
a fixed source of constant intensity the equations of motion of the disk are
Hamiltonian. In addition, in the case of a balanced circular disk the equations
of motion are integrable. A bifurcation analysis of the integrable case is
carried out. Using a scattering map, it is shown that the equations of motion
of the unbalanced disk are nonintegrable. The nonintegrability found here can
explain the complex motion of leaves in surface streams of bodies of water.
