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 Iteration basics Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/24/2008, 08:35 AM bo198214 Wrote:The Abel function counts the iterations of $f$: $\phi(f(f(x)))=\phi(f(x))+1=f(x)+2$ $\phi(f(f(f(x))))=\phi(f(f(x)))+1=f(x)+2+1=f(x)+3$ $\phi(f^{\circ n}(x))=\phi(x)+n$. The fact that Abel function extends COUNTING to non-integer , negative(?) and complex values of COUNTING is very interesting concept besides the fact it is useful in computations and analysis of iterates. $\phi(f^{\circ t}(x))=\phi(x)+t$. e.g. $\phi(f^{\circ I}(x))=\phi(x)+I$. If we turn it upside down, we can may be use the result of t iterations of a function to define what COUNTING with t (e.g. t=I) means. We may get functions which are only COUNTABLE in certain ways, so that Abel equation is not possible to solve for all t. Would that make sense? Ivars « Next Oldest | Next Newest »

 Messages In This Thread Iteration basics - by Ivars - 03/20/2008, 10:34 AM RE: Iteration basics - by Ivars - 03/20/2008, 05:24 PM RE: Iteration basics - by Gottfried - 03/21/2008, 08:37 AM RE: Iteration basics - by Ivars - 04/03/2008, 08:05 AM RE: Iteration basics - by Gottfried - 04/03/2008, 08:19 AM RE: Iteration basics - by Ivars - 04/03/2008, 10:13 AM RE: Iteration basics - by andydude - 04/05/2008, 11:35 PM RE: Iteration basics - by Gottfried - 04/06/2008, 07:16 AM RE: Iteration basics - by Ivars - 04/06/2008, 08:55 AM RE: Iteration basics - by andydude - 04/07/2008, 12:01 AM RE: Iteration basics - by Ivars - 04/20/2008, 10:15 PM RE: Iteration basics - by bo198214 - 04/21/2008, 08:21 PM RE: Iteration basics - by andydude - 04/22/2008, 05:30 AM RE: Iteration basics - by Ivars - 04/22/2008, 07:02 AM RE: Iteration basics - by Ivars - 04/09/2008, 07:56 PM RE: Iteration basics - by Ivars - 05/09/2008, 09:45 AM RE: Iteration basics - by bo198214 - 05/09/2008, 02:49 PM RE: Iteration basics - by Ivars - 05/27/2008, 10:33 AM RE: Iteration basics - by Gottfried - 05/27/2008, 07:35 PM RE: Iteration basics - by Ivars - 05/30/2008, 06:08 AM RE: Iteration basics - by Xorter - 01/02/2017, 05:21 PM RE: Imaginary iterates of exponentiation - by Gottfried - 03/20/2008, 12:04 PM RE: Imaginary iterates of exponentiation - by Ivars - 03/20/2008, 12:35 PM RE: Imaginary iterates of exponentiation - by bo198214 - 03/20/2008, 03:10 PM RE: Imaginary iterates of exponentiation - by Ivars - 05/24/2008, 08:35 AM RE: Imaginary iterates of exponentiation - by bo198214 - 05/24/2008, 09:04 AM RE: Imaginary iterates of exponentiation - by Gottfried - 05/24/2008, 09:47 AM RE: Imaginary iterates of exponentiation - by Ivars - 05/24/2008, 07:12 PM

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