# Theorem on increment of tetration

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Theorem on increment of superfunctionsis statement about asymptotic behavior of solution of the Transfer equation.

Let $$F$$ be solution of equation

$$F(z\!+\!1)=\exp\big(\beta F(z)\big)$$

for some $$\beta>0$$.

Let $$L$$ be the fixed point, id est, $$\exp(\beta L)=L$$

Let $$F(z)=L+\varepsilon+O(\varepsilon^2)$$

where $$\varepsilon = \exp(kz)$$ for some increment $$k$$.

Let $$~ K\!=\!\exp(k)$$

Then

$$\Im(K) = \Im(k)$$