  In this work we consider a class of endomorphisms of $\mathbb{R}^2$ defined
by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{R}$ is a real number and we prove that
when $-1<c<0$, the forward filled Julia set of $f$ is the union of stable
manifolds of fixed and $3-$periodic points of $f$. We also prove that the
backward filled Julia set of $f$ is the union of unstable manifolds of the
saddle fixed and $3-$periodic points of $f$.
