I was informed of the following geometric picture, and I would appreciate some references and details about it. Consider a family of elliptic curves converging to a self-intersecting rational curve $R$ over $\mathbb{CP}^1$ (so the elliptic curves are fibers over $\mathbb{C}$, and this rational curve $R$ is over $\infty$). Consider the subgroup $S_1\times \mathbb{Z}/n\mathbb{Z}$ for some $n$, where the $n$-torsion points lie on some of these circles, then one of these circles is "stable", as in it will converge to a circle on $R$, while other circles will converge to $\infty$ or $-\infty$ at different speed (the further from the stable circle, the faster?). I have also attached a drawing of the picture, and I would appreciate some texts about this. Is there any way to describe the speed how these circles converge to infinity, maybe using the parameter that describes the family?
