Mark McClure
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 Dec 7 comment Basins of attraction of equilibrium points As you have shown, the algebraic system $V_x=0,V_y=0$ has four numeric solutions and, if we apply Newton's method to that system, each of those solutions has an interesting basin of attraction. But that is a different question from whether those equilibrium points are attractive under a system of differential equations like $x'=V_x,y'=V_y$. Dec 7 comment Basins of attraction using Newton's method Part II I agree with Quantum_Oli - it would be nice to know where this came from. It appears there might be an interesting question here but the image looks like the Julia set of a polynomial - I can't imagine how your non-differentiable function generated it. Dec 7 comment Basins of attraction of equilibrium points I'm quite sure that the basins of attraction of Newton's method in two real variables have been well studied; there's an elementary discussion on pages 486-487 of Gil Strang's calculus text. If you're interested in studying the basins of attraction of the smooth dynamical system with a given potential, however, that's quite a different thing. Only one of your equilibrium points is attractive for that system. Dec 5 comment Basins of attraction using Newton's method The first thing my answer to that question does is generalize the code to arbitrary functions. I guess that's what @Saurav is referring to. Dec 3 awarded Good Answer Nov 15 awarded Nice Answer Nov 13 awarded Guru Nov 11 comment Can Mathematica Handle Open Intervals? Interval complements? @alancalvitti True - but, again, I don't think it's hard to roll your own depending on your needs. Nov 11 comment Can Mathematica Handle Open Intervals? Interval complements? @alancalvitti There is no such function that I know of, though it should be quite easy to create one using patterns. Something like `toInequality[Interval[{a_,b_}], var_] := a