Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points (Q2738076)

The paper deals with the scalings at the fixed point of Feigenbaum renormalization for non-standard families of unimodal maps. Namely, the mapping is allowed to be nonsymmetric near the critical point and the degree of the critical point itself is regarded as a parameter. The authors obtain explicit formulas for scalings in the asymptotic case when the degree of the critical point tends to 1. The asymptotics depend in an essential way on the asymmetry parameter and differ qualitatively from those obtained in the symmetric case.