I'd be greatly interested in a reference to the respective article. Was it Douady? Julia? Hubbard? Fatou? Bonus question: Who gave the proof that can be found in the [Orsay notes][1]? [1]: http://pi.math.cornell.edu/~hubbard/OrsayEnglish.pdf EDIT: The question was based upon a misconception on the asker's part: There are points in the Mandelbrot set whose Julia sets are NOT locally connected. Yet, all *interior* points of the Mandelbrot set have a locally connected Julia set. (There are boundary points of the Mandelbrot set whose Julia set is locally connected.)