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Let $\rho\colon\pi_1(T_1)\to PSL(2,\mathbb{C})$ be a faithful representation of the fundamental group of a once-punctured torus. If both the components of the convex core in the quotient manifold are three-times punctured spheres, then the limit set is made of an infinite union of circles which satisfy certain properties. Do you know where it is possible to find a nice description of this? I found this fact on a paper, but the references seem to be circular, and each one sends to a different paper which in turn sends to other ones, or to some mysterious preprint which I was not able to find. Could you help me, please?

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You could have a look at Indra's Pearls.

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