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In a recently completed paper Pascale Roesch and I have given a complete proof that the connectedness locus $M_{1}$ in the space moduli space of quadratic rational maps with a parabolic fixed point of multiplier 1 is homeomorphic to the Mandelbrot set. In this talk I will outline and discus the proof, which in an essential way involves puzzles and a theorem on local connectivity of $M_{1}$ at any parameter which is neither renormalizable nor has all fixed points non-repelling similar to Yoccoz celebrated theorem for local connectivity of $M$ at corresponding parameters.
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In a recently completed paper Pascale Roesch and I have given a complete proof that the connectedness locus $M_{1}$ in the space moduli space of quadratic rational maps with a parabolic fixed point of multiplier 1 is homeomorphic to the Mandelbrot set. In this talk I will outline and discus the proof, which in an essential way involves puzzles and a theorem on local connectivity of $M_{1}$ at any parameter which is neither renormalizable nor has ...
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37F46 ; 30D05 ; 37F31