On Thu, Jul 28, 2011 at 10:28 AM, Tom Karzes <karzes@sonic.net> wrote:
I believe this is what Mandelbrot was referring to. Here's another interview with him in which he talks very specifically about it:
I believe the conjecture he states there, and claims both that he originated and that no-one would have thought of without computer graphics, is the Fatou conjecture. I can't find a statement of the Fatou conjecture (which appears to be different from the "Fatou conjecture on wandering domains", since the former is unsolved and the latter proven). But the Real Fatou Conjecture (which has now been proved) appears to be exactly the same conjecture restricted to real values of c. Andy
Tom
Dan Asimov writes: > Suddenly two definitions of the Mandelbrot set come to mind, > the first one I learned (I), and the much more common one (II): > > For any c in C, define f_c(z) as z^2 + c. > > I. The set of c in C for which the Julia set of f_c is connected. > (See < http://en.wikipedia.org/wiki/Julia_set >.) > > II. the set of c in C for which the orbit of 0, under (forward) > iteration of f_c, is bounded. > > I've never seen a proof that these definitions are equivalent, > though I haven't looked very hard, either. (In II, it seems > to me that considering the orbits of 0 rather than of any > other point is somewhat arbitrary.) > > --Dan > > Sometimes the brain has a mind of its own. > > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >
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