  This paper studies properties of a Renormalization Operator for potentials in
symbolic dynamics. These operators first appeared in \cite{BLL} and the link
with substitutions was done in \cite{BL1}. Their fixed points are natural
candidates to have pathologic behavior such as phase transitions. If $R$ is
such an operator, we study the convergence of $R^{n}(\varphi)$ to the non-nul
fixed point.
  We define the family of marked substitutions, which contains the Thue-Morse
substitution, and show that the associated renormalization operators on
potentials admits a unique non-nul continuous fixed point. Then, we show that
$R^{n}(\varphi)$ converges to the fixed point as soon as $\varphi$ has the
right germ close to $\mathbb K$.
