We describe the well studied process of renormalization of quadratic polynomials from the point of view of their natural extensions. In particular, we describe the topology of the inverse limit of infinitely renormalizable quadratic polynomials and prove that when they satisfy a priori bounds, the topology is rigid modulo combinatorial equivalence.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-3,
author = {Carlos Cabrera and Tomoki Kawahira},
title = {Topology of the regular part for infinitely renormalizable quadratic polynomials},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {35-56},
zbl = {1192.37062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-3}
}
Carlos Cabrera; Tomoki Kawahira. Topology of the regular part for infinitely renormalizable quadratic polynomials. Fundamenta Mathematicae, Tome 209 (2010) pp. 35-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-3/