Are elliptical rings feasible?

Around a rocky planet or small gas giant, could there be a system of rings that follow an elliptical orbit? I have used a gravity simulator (this one) to test it, but the way it handles its particles doesn't seem like it would work. My question is, can a planet have an elliptical ring system?

This typically involves another orbiting body - say, a moon - creating, for instance, a Lindblad resonance with a subset of the particles in the ring that have the proper orbital period. These particles will be forced into slightly more eccentric orbits. While this has not occurred stably on a large scale in the present-day Solar System, it might occur in some circumstellar disks around other stars. The star Fomalhaut has a ring of dust of eccentricity $$e\simeq0.11\pm0.01$$ orbiting at a distance of $$a\simeq133\text{ AU}$$. The star is a couple hundred million years old, but the circularization timescale is only $$\tau\sim10^6$$ years. It has been suggested that the culprit is a planet orbiting at $$a_p\simeq119\text{ AU}$$, with an eccentricity similar to that of the disk (Quillen 2006). The theory holds up, but observations have not confirmed such an object.