On dynamical parameter space of cubic polynomials with a parabolic fixed point

Abstract This article focuses on the connectedness locus of the cubic polynomial slice with a parabolic fixed point of multiplier . We first show that any parabolic component, which is a parallel notion of hyperbolic component, is a Jordan domain. Moreover, a continuum called the central part in the connectedness locus is introduced. This is the natural analogue to the closure of the main hyperbolic component of . We prove that is almost a double covering of the filled‐in Julia set of the quadratic polynomial .