2
votes
2answers
291 views

Roadmap to Complex Dynamics (Particularly the works of Hubbard, Douady, and Yoccoz regarding the Mandelbrot set)

As others have had great success with their question, I hope to ask one in a similar vein. As a student who has some background in complex analysis and dynamical systems, I am hoping to explore ...
8
votes
2answers
466 views

How many times line segments can intersect a Jordan curve?

I posted a question on math.stackexchange.com but it seems this question might be open http://math.stackexchange.com/questions/109752/line-segments-intersecting-jordan-curve Namely, is there a set ...
16
votes
3answers
1k views

The deep significance of the question of the Mandelbrot set's local connectedness?

I am given to understand that the celebrated open problem (MLC) of the Mandelbrot set's local connectness has broader and deeper significance deeper than some mere curiosity of point-set topology. ...