This is my first question here so I don't know if I formatted this well. Please let me know how I could improve. So, I was messing around on desmos, specifically with composing functions n times.
An example:
Let $ f(x) = x^2 $ and $ S_n(x) = \underbrace{(f \circ f \circ f \: ... \: \circ \: f)}_{n \: \text{times}}(x) $
Then, $ S_n(x) = x^{2^n} $
I found that if I let $f(x) = cos(x)$ , the $ \lim_{n\to\infty} S_n(x) $ is equivalent to a constant function. (see the desmos link above for a model)
I am wondering what the limit is equal to and if it can be given in a closed form. (Using either elementary or non-elementary functions)
I will check back in this forum to answer any questions
