*The core chain of circles in the limit set of the Jorgensen's group *

**Abstract:**

We consider a sequence of punctured--torus groups, which gives a sequence of non degenerate 3-manifolds $M_n$, tending to a degenerate manifold $M$. We discuss property of the limit sets of $M_n$ and $M$. In particular, each limit set of $M_n$ contains a chain of tangent circles whose radii tend to $0$. The limit of these chains is a fractal curve in the limit set of $M$.