Topology of the regular part for infinitely renormalizable quadratic polynomials

2007/06/28 by Carlos Cabrera, Cabrera, Carlos, Tomoki Kawahira +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0706.4225

openalex publication_date 2007/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper 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 its combinatorics.

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