On the Break-Up of Invariant Tori with three Frequencies [chapter]

J. D. Meiss
1999 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