Slices of Parameter Space of Cubic Polynomials

In this paper, we study slices of the parameter space of cubic polynomials, up to affine conjugacy, given by a fixed value of the multiplier at a non-repelling fixed point. In particular, we study the location of the $main, cubioid$inthisparameterspace\mathrm{.}The$main, cubioid$ is the set of affine conjugacy classes of complex cubic polynomials that have certain dynamical properties generalizing those of polynomials $z^2+c$ for $c$ in the filled main cardioid.