Geodesic
Degenerations of invariant Lagrangian manifolds
Journal of Singularities, Tome 8 (2014), pp. 50-68

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We consider a pair (H, I) where I is an involutive ideal of a Poisson algebra and H in I. We show that if I defines a "2n-gon singularity", then, under arithmetical conditions on H, any deformation of H can be integrated as a deformation of (H, I). 
@article{10_5427_jsing_2014_8e,
     author = {Mauricio Garay},
     title = {Degenerations of invariant {Lagrangian} manifolds},
     journal = {Journal of Singularities},
     pages = {50--68},
     publisher = {mathdoc},
     volume = {8},
     year = {2014},
     doi = {10.5427/jsing.2014.8e},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.8e/}
}
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Mauricio Garay. Degenerations of invariant Lagrangian manifolds. Journal of Singularities, Tome 8 (2014), pp. 50-68. doi: 10.5427/jsing.2014.8e

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