Difference between revisions
mlc-conjecture
Status and infobox
- status:
—→ open - kind:
—→ problem - year:
—→ 1980 - statement:
—→ The Mandelbrot set is locally connected.
Source +22 −0
+---
+title: 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.
+space: dynamics
+---
+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)
+
+[[Space:dynamics|Dynamical systems]] · [[Continent:mathematics|Mathematics]]
Revision 56 as rendered
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