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Cubic polynomials with a parabolic point

Published online by Cambridge University Press:  22 January 2010

P. ROESCH
P. ROESCH*
Affiliation:
IMT, Toulouse, France (email: pascale.roesch@math.univ-toulouse.fr)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 6 , December 2010 , pp. 1843 - 1867
Copyright
Copyright © Cambridge University Press 2009

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