Cassini ovals are a well-known family of quartic curves which include the lemniscate as a special case. They can be thought as the vertical cross sections of a torus, that is, the intersections of a torus and a plane (picture taken from Tristan Needham's Visual Complex Analysis):
Is there a name for the family of curves obtained by intersecting a n-holed torus and a plane in a similar fashion? By n-holed torus I mean the connected sum of n tori, where n is any natural number:
The reason I'm asking is that such curves seem to appear in the phase portrait of a pendulum, and I was curious to know more about them:
