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TY - CHAP
TI - Fixed points of renormalization
A2 - McMullen, Curtis T.
AB - 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 polynomial*f*whose inner class is fixed under renormalization. We show that if the quadratic germs of$\mathcal{R}_{p}^{n}(f)$have

EP - 134
PB - Princeton University Press
PY - 1996
SN - 9780691011530
SP - 119
T2 - Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142)
UR - http://www.jstor.org/stable/j.ctt7ztfmd.9
Y2 - 2021/09/18/
ER -