Familles d'équations de Thue associées à un sous-groupe de rang 1 d'unités totalement réelles d'un corps de nombres

Abstract: Let $F$ be an irreducible binary form attached to a number field $K$ of degree $\geq 3$. Let $\epsilon\not\in {-1, 1}$ be a totally real unit of $K$. By twisting $F$ with the powers $\epsilon^a$ of $\epsilon$, ($a\in{\mathbf Z}$), we obtain an infinite family $F_a$ of binary forms. Let $m\in{\mathbf Z}$. We give an effective bound for $\max{|a|, \log|x|, \log|y|}$ when $a,x,y$ are rational integers satisfying $F_a(x,y)=m$ with $xy\not=0$.