High Quality Content by WIKIPEDIA articles! Equations such as Schroder's have been extensively utilized in studies of nonlinear dynamics, which has often referred to colloquially as chaos theory. It is used in studies of turbulence. The change of variables ?(x)=log(f(x))/log(c) converts Schroder's equation to the older Abel equation, ?(h(x))=?(x)+1. The fifth problem on Hilbert's list is a generalisation of this equation.We prove below that any other solutions must be highly pathological functions.

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