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## Analytic invariants for the \$1:-1\$ resonance

### Abstract

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
OAI identifier: oai:arXiv.org:1105.1349