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What is the attracted locus in this recursion?

Consider $R: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ given by $R(a,b) = (b,2.5b-a).$ Let $p_0 = (x_0, y_0)$ be arbitrary and $p_{i+1} = R(p_i).$ Most starting points $p_0$ give a divergent path. One ca …