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Asymptotics of one function on natural numbers
Posted:
May 3, 2013 9:31 PM


Below, N is the set of natural numbers.
Consider a function s: N>N such that s(x) = x + 1. Now, if f: N>N is an arbitrary function, define a mapping from the set of all such functions to N as given below:
p(f) = c(1)
where c is the composition of functions s and f.
Finally, define a new function g: N>N such that
g(x) = f(x) for all x != f^n(x) g(x) = p(f) otherwise.
We will use a shorthand notation g = F(f) for the function g defined above.
Consider now the sequence of F repeatedly applied: F, F(F(f)),..., F^k(f),...
Question: how one will study the asymptotics of F^k at k>infinity for various n and p?
Thanks, Dmitri



