  We present three-dimensional SPH calculations of giant planets embedded in
gaseous disks. Our findings are collected into a map of parameter space,
exhibiting four distinct regions: Type I migration, gap formation, triggered
formation of more planets, and wholly unstable disks. For Type I migration of
the planet due to secular interactions with the disk material, the migration
rate depends linearly on the disk mass, and is independent of the initial
planet mass. For more massive disks, the planet can disturb the disk strongly
enough to trigger the collapse of gas into additional giant planets. When
additional planets form, their interaction as point masses dominates the
subsequent behavior of the system. This mechanism allows for the rapid
formation of Jupiter-mass and higher planets. Migration due to interaction with
the disk can significantly change the orbits of giant planets in gas disks.
