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 elementary superfunctions Kouznetsov Fellow Posts: 151 Threads: 9 Joined: Apr 2008 04/25/2010, 11:35 AM (This post was last modified: 04/25/2010, 12:03 PM by Kouznetsov.) (04/25/2010, 10:48 AM)bo198214 Wrote: Challenge: Is there an elementary superfunction of a polynomial that has no real fixed point?I thnk so. How about transformation of line 5, $b=2$? Let $H_0(z)=z^2$ ; $P(z)=z+1$; $Q(z)=z-1$; Let $H_1(z)=P(H_0(Q(z)))=1+(z-1)^2$; Equation $z=1+z^2-2z+1$; (BAD)is equivalent of equation $z^2-z+2=0$ (BAD)Gives the fixed points $z=1/2 \pm \sqrt{1/4-2}=1/2\pm i \sqrt{7/4}$ Sorry I lost the signum! should be is equivalent of equation $z^2-3z+2=0$ Gives the fixed points $z=1/2 \pm \sqrt{9/4-2}=1/2\pm \sqrt{1/4}$ I try again: $P(z)=z+a$; $Q(z)=z-a$; Let $H_1(z)=P(H_0(Q(z)))=a+(z-a)^2$; Equation $z=a+z^2-2az+a^2$; is equivalent of equation $z^2-(2a+1)z+a^2+a=0$ Gives the fixed points $z=(2a+1)/2 \pm 1/2\sqrt{(4a^2+4a+1-4(a+a^2)}$ $z=(2a+1)/2 \pm 1/2\sqrt{1}$ Henryk, it is not so easy... Sorry... but.. Wait... May I use complex $a$ or the basefunction is supposed to be real? Do you mean "real polynomial"? « Next Oldest | Next Newest »

 Messages In This Thread elementary superfunctions - by bo198214 - 04/23/2009, 01:25 PM RE: elementary superfunctions - by bo198214 - 04/23/2009, 02:23 PM RE: elementary superfunctions - by bo198214 - 04/23/2009, 03:46 PM RE: elementary superfunctions - by tommy1729 - 04/27/2009, 11:16 PM RE: elementary superfunctions - by bo198214 - 04/28/2009, 08:33 AM RE: elementary superfunctions - by bo198214 - 03/27/2010, 10:27 PM RE: elementary superfunctions - by bo198214 - 04/18/2010, 01:17 PM RE: elementary superfunctions - by tommy1729 - 04/18/2010, 11:10 PM RE: elementary superfunctions - by bo198214 - 04/25/2010, 08:22 AM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 09:11 AM RE: elementary superfunctions - by bo198214 - 04/25/2010, 09:23 AM RE: elementary superfunctions - by bo198214 - 04/25/2010, 10:48 AM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 11:35 AM RE: elementary superfunctions - by bo198214 - 04/25/2010, 12:12 PM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 12:42 PM RE: elementary superfunctions - by bo198214 - 04/25/2010, 01:10 PM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 01:52 PM Super-functions - by Kouznetsov - 05/11/2009, 02:02 PM [split] open problems survey - by tommy1729 - 04/25/2010, 02:34 PM RE: [split] open problems survey - by bo198214 - 04/25/2010, 05:15 PM

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