Hyperbolicity is dense in the real quadratic family

1992/07/06 by Grzegorz Świa̧tek, Swiatek, Grzegorz · 1 citation
Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.math/9207219

openalex publication_date 1992/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that for non-hyperbolic real quadratic polynomials topological and quasisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that hyperbolic maps are dense.

Citations

• The boundary correspondence under quasiconformal mappings

Cited by

• Absorbing Cantor sets in dynamical systems: Fibonacci maps

Related

• Hyperbolicity and Quasi-hyperbolicity in Polynomial Diffeomorphisms of \Bbb C²
• Quadratic Dynamics Over Hyperbolic Numbers
• Geometry of quadratic polynomials: moduli, rigidity and local connectivity
• Density of hyperbolicity of real Newton maps
• Dynamics of quadratic polynomials II: rigidity