# MLC: the Mandelbrot set is locally connected

- kind: problem
- status: open
- year: 1980
- authors: Adrien Douady and John H. Hubbard

**Statement.** The Mandelbrot set is locally connected.

If true, the Mandelbrot set's whole structure would be described by a simple combinatorial model, pinched disks, and hyperbolicity would be dense among quadratic maps. Yoccoz proved local connectivity at many points, and Jeremy Kahn and Mikhail Lyubich extended it. The full conjecture is open.

Posed 1980s, Adrien Douady and John H. Hubbard.

## What would settle it

Lean statement in formal-conjectures

## Sources

- [Wikipedia: Mandelbrot set](https://en.wikipedia.org/wiki/Mandelbrot_set)

[Dynamical systems](/wiki/Space:dynamics.md) · [Mathematics](/wiki/Continent:mathematics.md)

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