Equivariant normal form for nondegenerate singular orbits of integrable hamiltonian systems
By Eva Miranda, Nguyen Tien Zung. 2003
97 citations recorded by the source corpus.
We consider an integrable Hamiltonian system with n degrees of freedom whose first integrals are invariant under the symplectic action of a compact Lie group G. We prove that the singular Lagrangian foliation associated to this Hamiltonian system is symplectically equivalent, in a G-equivariant way, to the linearized foliation in a neighborhood of a compact singular nondegenerate orbit. We also show that the nondegeneracy condition is not equivalent to the nonresonance condition for smooth systems.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ba1f422b5144bdf4a48857eb450ed0319239f010
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Citations in the corpus
- Semitoric integrable systems on symplectic 4-manifolds (2008, background): “To conclude the proof it suffices to show that ψ(1) ◦ψ−1 ∈ 0, because once we know this (2) will follow from Theorem 3.2 in Miranda-Zung2 [20]: The exponential exp : g −→ 0 is a surjective group homomorphism, and moreover there is an explicit right inverse given by φ ∈ 0 −→ ∫ 1 0 Xtdt ∈ g where Xt ∈”
- Smooth normal forms for integrable Hamiltonian systems near a focus–focus singularity (2011, unknown): “4 ([6]).”
- Constructing integrable systems of semitoric type (2009, methodology): “Furthermore, many works have played an important role in our investigation of 4-dimensional semitoric systems, by serving as stepping stones to construct the symplectic invariants in [20] associated with semitoric systems; nota bly we used work of Dufour-Molino [8], Eliasson [9], Duistermaat [7], Mi”