2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69276Given a critically periodic quadratic map with no secondary renormalizations, we introduce the notion of $Q$-recurrent quadratic polynomials. We show that the pieces of the principal nest of a $Q$-recurrent map $f_c$ converge in shape to the Julia set of $Q$. We use this fact to compute analytic invariants of the nest of $f_c$, to give a complete characterization of complex quadratic Fibonacci maps and to obtain a new auto-similarity result on the Mandelbrot set.8 figuresDynamical Systems37F20text