# Difference between revisions of "Theorem on increment of tetration"

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[[Theorem on increment of superfunctions]]is statement about asymptotic behavior of solution of the [[Transfer equation]]. |
[[Theorem on increment of superfunctions]]is statement about asymptotic behavior of solution of the [[Transfer equation]]. |
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Let \(F\) be solution of equation |
Let \(F\) be solution of equation |

## Revision as of 01:22, 11 August 2020

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

## Statement

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**

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

## References