A family of cubic rational maps and matings of cubic polynomials

Abstract

We study a family of cubic branched coverings and matings of cubic polynomials of the form g ╨ f, with g = ga: z ↦ z3 + a and f = Pi for i = 1, 2, 3 or 4. We give criteria for matability or not of critically finite ga with each Pi. The maps ga ╨ P1 illustrate features that do not occur for matings of quadratic polynomials: they never have Levy cycles but do sometimes have Thurston obstructions. © A K Peters, Ltd.