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Recently I have read a proof of the Perron Frobenius Theorem for positive aperiodic matrices. In this proof, the trick is to put a metric in the "positive quadrant" of $\mathbb{R}^n$, $\mathbb{R}^{n}_+...

Let $z \in \mathbb R\backslash \left\{2 \right\}$ then I would like to understand the following: Consider the dynamical system with $x_i \in \mathbb C^2:$ $$ x_{i} = \left(\begin{matrix} z &&...