Parabolic limits of renormalization
Abstract
In this paper we give a combinatorial description of the renormlization limits of infinitely renormalizable unimodal maps with essentially bounded combinatorics admitting quadratic-like complex extensions. As an application we construct a natural analogue of the period-doubling fixed point. Dynamical hairiness is also proven for maps in this class. These results are proven by analyzing parabolic towers: sequences of maps related either by renormalization or by parabolic renormalization.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.