Lyapunov instability in KAM stable Hamiltonians with two degrees of freedom

Abstract

For a fixed frequency ω P R 2 zt0u we show the existence of Gevrey smooth Hamiltonians, arbitrarily close to a Kolmogorov non-degenerate analytic Hamiltonian, having a Lyapunov unstable elliptic equilibrium with frequency ω. In particular, the Hamiltonians thus constructed will be KAM-stable.