Rigidity of non-renormalizable Newton maps

2018/11/25 by Pascale Roesch, Roesch, Pascale, Yongcheng Yin +3 · 4 citations
Mathematics · #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1811.09978

Abstract

Non-renormalizable Newton maps are rigid. More precisely, we prove that their Julia set carries no invariant line fields and that the topological conjugacy is equivalent to quasi-conformal conjugacy in this case.

Cited by

• Gluing polynomials along the circle
• Density of hyperbolicity of real Newton maps
• Most Fatou and Julia components are small for polynomials
• Boundary of the central hyperbolic component I: dynamical properties

Related

• Rigidity of Newton dynamics
• Local rigidity of Schottky maps
• No invariant line fields on Cantor Julia sets
• Quadratic and cubic Newton maps of rational functions
• A rigidity estimate for maps from S² to S² via the harmonic map flow