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Analytic invariants for the $1:-1$ resonance

By Jose Pedro Gaivao


Associated to analytic Hamiltonian vector fields in $\mathbb{C}^4$ having an equilibrium point satisfying a non semisimple $1:-1$ resonance, we construct two universal constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.Comment: 48 pages, 5 figure

Topics: Mathematics - Dynamical Systems, 37J20, 34M40
Year: 2013
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