  We prove a priori bounds for Feigenbaum quadratic polynomials, i.e.,
infinitely renormalizable polynomials $f_c: z\mapsto z^2+c$ of bounded type. It
implies local connectivity of the corresponding Julia sets $J(f_c)$ and MLC
(local connectivity of the Mandelbrot set) at the corresponding parameters $c$.
It also yields the scaling Universality, dynamical and parameter, for the
corresponding combinatorics. The MLC Conjecture was open for the most classical
period-doubling Feigenbaum parameter as well as for the complex tripling
renormalizations. Universality for the latter was conjectured by
Goldberg-Khanin-Sinai in the early 1980s.
