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Douady–Hubbard mateability conjecture for quadratic polynomials
Douady–Hubbard's conjecture. The points $c_1$ and $c_2$ do not lie in conjugate limbs of the Mandelbrot set if and only if
Conjectureopenmandelbrot-set polynomial-matings quadratic-dynamicsarXiv posted 3 days ago

Douady–Hubbard mateability conjecture for quadratic polynomials