Dynamics of quadratic polynomials II: rigidity
arXiv:math/9512229
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.
References in corpus (6)
- Local connectivity of Julia sets: expository lectures
- On the Lebesgue measure of the Julia set of a quadratic polynomial
- Geometry of quadratic polynomials: moduli, rigidity and local connectivity
- Hyperbolicity is dense in the real quadratic family
- Quasisymmetric conjugacies between unimodal maps
- Dynamics of quadratic polynomials, I: Combinatorics and geometry of the Yoccoz puzzle