A simple proof of Sullivan's complex bounds

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Genadi Levin
DOI: 10.48550/arxiv.2601.21326
Cited by: 0

Abstract

About 35 years ago Dennis Sullivan proved a precompactness property ("complex bounds") for infinitely renormalizable real quadratic polynomials with bounded combinatorics. We present a simple "soft" proof of this remarkable result.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Advanced Differential Equations and Dynamical Systems Geometric and Algebraic Topology

Publication details

Journal / source
arXiv (Cornell University)
Publication date
29 January 2026
Document type
Preprint