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Aymptotically stable?

  1. Apr 6, 2006 #1
    Suppose F and G are [tex]c^2[/tex] and [tex] F_x = F_y = G_x = G_y = 0 [/tex] at the origin. Must the origin be an asymptotically stable equilibrium point?

    One more

    Give an explicit example of a DE with exactly two saddle points and no other equilibria. Anybody? Could I work backwards starting with the eigenvalues to form a system that has the two saddle points? This might be a dumb question.
     
  2. jcsd
  3. Apr 7, 2006 #2

    HallsofIvy

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    It would help a lot if you would actually state the problem clearly.
    Without the requirement that dx/dt= F(x,y) and dy/dt= G(x,y), which you don't say, the problem makes no sense at all. Given that, what about F(x,y)= G(x,y)= 1. Is the origin even an equilibrium point?
     
  4. Apr 7, 2006 #3
    This was just posed as a review question on a "things to know sheet". There weren't any specific details. Oh well. Too late. Test in 40 minutes.
     
  5. Apr 7, 2006 #4

    HallsofIvy

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    Presumably, then, you were expected to know what material was being reviewed or at least what course this is- things WE do not know!
     
  6. Apr 7, 2006 #5
    Did you REALLY have to state the obvious?
     
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