I am a condensed matter physicist, and want to understand the Hopf link from analytic point of view. My question is as follows.

We have two sets of equations, and each set of equations describes a circle in certain space, for example in $\mathbb{R}^3$. In that case, how can we tell from the equations if the two circles are linked, and whether the link is a Hopf link? I want the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?