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In 1994, P.-G. Becker and W. Bergweiler listed all the differentiallyalgebraic solutions of three famous functional equations: the Schr{\"o}der's,B{\"o}ttcher's and Abel's equations. The proof of this theorem combines variousdomains of mathematics. This goes from the theory of iteration, which gavebirth to these equations, to the algebro-differential notion of coherentfamilies developed by M. Boshernitzan and L. A. Rubel. This survey is anexcursion into the history of these equations, in order to enlighten thedifferent pieces of mathematics they bring together and how these parts fitinto the result of P.-G. Becker and W. Bergweiler.

A survey on the hypertranscendence of the solutions of the Schr\"oder's, B\"ottcher's and Abel's equations