Abstract
In this paper, we define a notion of parabolic ray which is analogous to external/internal ray in super-attracting basins. It is used to construct parabolic puzzles similar to Yoccoz puzzles, but modified near the parabolic fixed point. As an application, we show that any non-renormalizable quadratic rational map in the connectedness locus M 1 of Per1(1) has locally connected Julia set.
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