Is there any ways to compute iterations of a oscillating function ?

[Shanghai46]

So we all know we can use fixed point to calculate iterations. Functions that converge to a real value, then using Schroeder's equation to compute it.
But, when the function converges to a oscillating pattern? When the upper limit and downwards limit converges, and it keeps oscillating between the 2 (like for \({^x}a\) when \(a\) is between \(0\) and \(e^{-e}\)), is there a way, an equation to compute it?

The only way I've found to do so, is with function that converge into the negative iterations and oscillates in the positive (or vice versa if you use the inverse function). You compute it on the converging side, then apply the inverse function, but it's kinda cheating...

[Shanghai46]

The best way is to converge on the function could be using a oscillating diagram or by tetrating the limit and the maximum of the equation until it's over.

Ummmm......What?

[tommy1729]

One way is using sin or cos 


For instance 

https://tetrationforum.org/showthread.php?tid=1622

Bo and Leo and others went into this in various places.


regards

tommy1729

[tommy1729]

One way is using sin or cos 


For instance 

https://tetrationforum.org/showthread.php?tid=1622

Bo and Leo and others went into this in various places.


regards

tommy1729

btw , the links are dead but just paste the (thread identifation numbers) tid numbers and you can get there !

( because the name of the domain changed )


regards

tommy1729