  Context. Transition disks typically appear in resolved millimeter
observations as giant dust rings surrounding their young host stars. More
accurate observations with ALMA have shown several of these rings to be in fact
asymmetric: they have lopsided shapes. It has been speculated that these rings
act as dust traps, which would make them important laboratories for studying
planet formation. It has been shown that an elongated giant vortex produced in
a disk with a strong viscosity jump strikingly resembles the observed
asymmetric rings.
  Aims. We aim to study a similar behavior for a disk in which a giant planet
is embedded. However, a giant planet can induce two kinds of asymmetries: (1) a
giant vortex, and (2) an eccentric disk. We studied under which conditions each
of these can appear, and how one can observationally distinguish between them.
This is important because only a vortex can trap particles both radially and
azimuthally, while the eccentric ring can only trap particles in radial
direction.
  Methods. We used the FARGO code to conduct the hydro-simulations. We set up a
disk with an embedded giant planet and took a radial grid spanning from 0.1 to
7 times the planet semi-major axis. We ran the simulations with various
viscosity values and planet masses for 1000 planet orbits to allow a fully
developed vortex or disk eccentricity. Afterwards, we compared the dust
distribution in a vortex-holding disk with an eccentric disk using dust
simulations.
  Results. We find that vorticity and eccentricity are distinguishable by
looking at the azimuthal contrast of the dust density. While vortices, as
particle traps, produce very pronounced azimuthal asymmetries, eccentric
features are not able to accumulate millimeter dust particles in azimuthal
direction, and therefore the asymmetries are expected to be modest.
