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Hyperbolicity is dense in the real quadratic family

Grzegorz Swiatek
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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.

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Grzegorz Swiatek. 1992-07-06. Hyperbolicity is dense in the real quadratic family. https://arxiv.org/abs/math/9207219

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