Institute for Mathematical Sciences

Preprint ims95-14

M. Lyubich
Dynamics of quadratic polynomials II: Rigidity.

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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