Homeomorphisms between limbs of the Mandelbrot set
classification
🧮 math.DS
keywords
mandelbrothyperboliclimbsbackcomponentcomponentsconjecturedenominators
read the original abstract
We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic components. This settles a conjecture on the Mandelbrot set that goes back to 1994.
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