Abstract
We study germs of analytic Poisson structures which are suitable perturbations of a quasihomogeneous Poisson structure in a neighborhood of the origin of ℝn or ℂn, a fixed point of the Poisson structures. We define a “diophantine condition” relative to the quasihomogeneous initial part ie256-1 which ensures that such a good perturbation of 256-2 which is formally conjugate to 256-3 is also analytically conjugate to it.
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To V.I. Arnold on the occasion of his 70th birthday
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Stolovitch, L. Rigidity of Poisson structures. Proc. Steklov Inst. Math. 267, 256–269 (2009). https://doi.org/10.1134/S008154380904021X
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DOI: https://doi.org/10.1134/S008154380904021X