Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points

The universal period-doubling scaling of a unimodal map with an asymmetric critical point is governed by a period-2 point of a renormalisation operator. The period-2 point is parametrised by the degree of the critical point and the asymmetry modulus. In this paper we study the asymptotics of period-2 points and their associated scaling parameters in the singular limit of degree tending to 1.