Local connectivity and quasi‐conformal rigidity of non‐renormalizable polynomials

By Oleg Kozlovski, Sebastian van Strien. 2006

89 citations recorded by the source corpus.

We prove that topologically conjugate non‐renormalizable polynomials are quasi‐conformally conjugate. From this we derive that each such polynomial can be approximated by a hyperbolic polynomial. As a by‐product we prove that the Julia set of a non‐renormalizable polynomial with only hyperbolic periodic points is locally connected, and the Branner–Hubbard conjecture. The main tools are the enhanced nest construction (developed in a previous joint paper with [Rigidity for real polynomials, Ann. of Math. (2) 165 (2007) 749–841.]) and a lemma of Kahn and Lyubich (for which we give an elementary proof in the real case).

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b52fcfdf5c0adf0341bb9e2a52ea937fd0115835

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In Applied Mathematics

1. Juan Rivera-Letelier
2. F. Przytycki

In Geometry and Topology

1. F. Przytycki
2. Juan Rivera-Letelier

In Mathematical Physics

1. F. Przytycki
2. Juan Rivera-Letelier

Citations in the corpus

• Nice Inducing Schemes and the Thermodynamics of Rational Maps (2008, background): “Let f an at most finitely renormalizable polynomial, and consider the puzzle constriction described in [ KvS06 , §2.1].”