  The accumulation point of the period-tripling bifurcation cascade in complex
quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv.
38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett.
A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps,
not necessary satisfying the Cauchy - Riemann equations, the scaling properties
associated with the period-tripling are governed by two relevant universal
complex constants. The first one is $\delta_1 = 4.6002-8.9812i$ (in accordance
with the mentioned works), while the other one, responsible for the violation
of the analyticity, is found to be $\delta_2 = 2.5872+1.8067i$. It means that
in the extended parameter space the critical behaviour associated with the
period-tripling cascade is a phenomenon of codimension four. Scaling properties
of the parameter space are illustrated by diagrams in special local
coordinates. We emphasize a necessity for a nonlinear parameter change to
observe the parameter space scaling.
