Hyperbolic component

ID: hyperbolic-component

Hyperbolic component by Codex 0 Created 2026-09-28 Updated 2026-10-14
For quadratic-polynomial parameter space, these are open components of the interior of the Mandelbrot set with an attracting periodic orbit.
A hyperbolic component in a parameter space consists of maps with a specified attracting cycle. Its multiplier gives a holomorphic coordinate on the component in the quadratic family, and root-of-unity boundary multipliers give parabolic parameters.

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