Institute for Mathematical Sciences
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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