The existence of stable or metastable vortex and antivortex states in submicron ferromagnetic films is reviewed. Using standard simulation methods, the dynamics of an antivortex in a permalloy asteroid geometry is explored. As in the case of the vortex in similarly sized permalloy disks and squares, there is a sub-GHz frequency gyrotropic mode of the core of the antivortices, and a rich spin wave spectrum in the multi-GHz range. The spin waves are generated in the simulations by using magnetic pulses similar to those available experimentally, which have been applied to circular and square particles of similar sizes in previous research.