  In this paper we study an action of the absolute Galois group $\Gamma$ on
bicolored plane trees induced by the action of $\Gamma$ on equivalence classes
of conservative polynomials which are the simplest example of postcritically
finite rational functions. We establish some basic properties of this action
and compare it with the similar action provided by the Grothendieck theory of
"Dessins d'enfants".
