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.
This is a pre-print. The definitive version: MESTEL, B.D. and OSBALDESTIN, A.H., 2000. Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points. Journal of Mathematical Physics, 41 (7), pp.4732-4746, is available at: http://jmp.aip.org/.