  We study the dynamics of inertial particles in two dimensional incompressible
flows. The Maxey-Riley equation describing the motion of inertial particles is
used to construct a four dimensional dissipative bailout embedding map. This
map models the dynamics of the inertial particles while the base flow is
represented by a 2-d area preserving map. The dynamics of particles heavier
than the fluid, the aerosols, as well as that of bubbles, particles lighter
than the fluid, can be classified into 3 main dynamical regimes - periodic
orbits, chaotic structures and mixed regions. A phase diagram in the parameter
space is constructed with the Lyapunov characteristic exponents of the 4-d map
in which these dynamical regimes are distinctly identified. The embedding map
can target periodic orbits, as well as chaotic structures, in both the aerosol
and bubble regimes, at suitable values of the dissipation parameter.
