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Lyapunov instability in KAM stable Hamiltonians with two degrees of freedom
For a fixed frequency vector $ω\in \mathbb{R}^2 \, \setminus \, \lbrace 0 \rbrace$ obeying $ω_1 ω_2 < 0$ we show the existence of Gevrey-smooth Hamiltonians, arbitrarily close to an integrable Kolmogorov non-degenerate analytic Hamiltonian, having a Lyapunov unstable elliptic equilibrium with freque
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