Geometry of Q-recurrent maps

Original · EN

Given 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 fc converge in shape to the Julia set of Q. We use this fact to compute analytic invariants of the nest of fc, to give a complete characterization of complex quadratic Fibonacci maps and to obtain a new auto-similarity result on the Mandelbrot set.