the triangle $CQS$. The union of the two triangles is invariant as the dotted images $ODB$ and $CSQ$ show, as is the line of fixed points $OS$. Hence in this case we have $$\ell(X^+)=-\alpha A= |\alpha A|.$$ A similar argument (with extra triangles) can be used to show that for $0<A \leq 1$ and $$-2 < \frac{-2}{1+A} \leq \alpha<-1$$ the maximal invariant set has measure $$\ell(X^+)=-\frac{\alpha A}{2},$$ but we omit this for conciseness.

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