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Cubic polynomials with a parabolic point
Published online by Cambridge University Press: 22 January 2010
Abstract
We consider cubic polynomials with a simple parabolic fixed point of multiplier 1. For those maps, we prove that the boundary of the immediate basin of attraction of the parabolic point is a Jordan curve (except for the polynomial z+z3 where it consists in two Jordan curves). Moreover, we give a description of the dynamics and obtain the local connectivity of the Julia set under some assumptions.
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- Copyright © Cambridge University Press 2009
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