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Hamiltonian Systems with Three or More Degrees of Freedom
We construct an approximate renormalization operator for a two and one half degree of freedom Hamiltonian corresponding to an invariant torus with a frequency in the cubic field Q(τ), where τ 3 +τ 2 -2τ-1=0. This field has irrational vectors that are most robust in the sense of supremal Diophantine constant. Our renormalization operator has a critical fixed point, but it is not hyperbolic. Instead it has a codimension three stable manifold with one unstable eigenvalue, δ≈2.88, and two neutral eigenvalues.doi:10.1007/978-94-011-4673-9_64 fatcat:fascb6k2xfd2dijxhqdujl5acu