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Suppose you have the following coupled discrete dynamical system: \begin{align*} e_{k+1}&=e_k - 2~\alpha~e_k~\lambda^2~\alpha_k^2 + \alpha^2~e_k^2~\lambda^3 \alpha_k^3\\ \alpha_{k+1}&= \...

Is the following statement true? How it can be proved/rejected? Initial conditions that correspond to unbounded orbits in polynomial symplectic mappings, which exhibit chaotic behavior (exponential ...