Local topology of cubic Newton, methods: the parameter plane

Cubic Newton's methods are rational maps having three distinct super-attracting fixed points and a single free critical point. They form, rep to conjugation, a family N-lambda parametrized by Lambda = C\{0, +/-3/2}, and we denote by H-0 the set of lambda for which the free critical point of N-lambda is in the immediate basin of one of the super-attracting fixed points. In this Note, we show that the boundary of each connected component of H-0 is a Jordan curve. For this, we determine in Lambda regions on which the dynamics of N-lambda can be described by a fixed combinatorial model. (C) Academie des Sciences/Elsevier, Paris.