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 question about regular iteration, also about tetration properties in general bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 05/04/2009, 07:34 AM (This post was last modified: 05/04/2009, 07:35 AM by bo198214.) (05/04/2009, 04:23 AM)Tetratophile Wrote: (05/03/2009, 07:05 AM)bo198214 Wrote: Its regular if the iterates are differentiable (or at leas asymptotically differentiable) at the fixed point. This implies that $(f^{[t]})'(x_0) = f'(x_0)^t$. do you mean that the derivative of the function iterated $t$ times at the fixed point is the derivative at the fixed point to the $t^{th}$ power (multiplied t times)? exactly. You see that is satisfied for natural numbered iterations: $(f^{[2]})'(x_0)=f'(f(x_0)) f'(x_0)= f'(x_0)^2$ $(f^{[3]})'(x_0)= ...$ $(f^{[n+1]})'(x_0) = f'(f^{[n]}(x_0)) (f^{[n]})'(x_0) = f'(x_0) f'(x_0)^n = f'(x_0)^{n+1}$. « Next Oldest | Next Newest »

 Messages In This Thread question about regular iteration, also about tetration properties in general - by Base-Acid Tetration - 05/03/2009, 02:49 AM RE: question about regular iteration - by bo198214 - 05/03/2009, 07:05 AM RE: question about regular iteration - by Base-Acid Tetration - 05/04/2009, 04:23 AM RE: question about regular iteration - by bo198214 - 05/04/2009, 07:34 AM RE: question about regular iteration - by Base-Acid Tetration - 05/05/2009, 03:27 AM RE: question about regular iteration - by bo198214 - 05/10/2009, 09:32 AM

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