@inbook{10.2307/j.ctt7ztfmd.9,
ISBN = {9780691011530},
URL = {http://www.jstor.org/stable/j.ctt7ztfmd.9},
abstract = {In this chapter we study the convergence of iterated renormalization over the complex numbers.We begin by defining the renormalization operators${{\mathcal{R}}_{p}}$and discussing their relation to tuning and the Mandelbrot set. Then we give a conjectural construction of fixed points of renormalization, starting from purely combinatorial data, namely a quadratic polynomial with a periodic critical point. The construction parallels the geometrization of 3-manifolds that fiber over the circle.Next we justify several steps in the construction, starting with a quadratic polynomialfwhose inner class is fixed under renormalization. We show that if the quadratic germs of$\mathcal{R}_{p}^{n}(f)$have},
bookauthor = {Curtis T. McMullen},
booktitle = {Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142)},
pages = {119--134},
publisher = {Princeton University Press},
title = {Fixed points of renormalization},
year = {1996}
}