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Dynamics of quadratic polynomials II: rigidity

Mikhail Lyubich
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Abstract

This is a continuation of the series of notes on the dynamics of quadratic polynomials. We show the following Rigidity Theorem: Any combinatorial class contains at most one quadratic polynomial satisfying the secondary limbs condition with a-priori bounds. As a corollary, such maps are combinatorially and topologically rigid, and as a consequence, the Mandelbrot set is locally connected at the correspoinding parameter values.

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Mikhail Lyubich. 1995-12-01. Dynamics of quadratic polynomials II: rigidity. https://arxiv.org/abs/math/9512229

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