Rigidity of Poisson structures (Q600704)

The main result of the paper under review provides conditions ensuring that suitable analytic perturbations of a quasihomogeneous Poisson structure \({\mathcal L}\) are analytically conjugate to \({\mathcal L}\) as soon as they are formally conjugate to \({\mathcal L}\). Loosely speaking, the corresponding sufficient conditions consist in the requirement that the spectrum of a certain linear self-adjoint operator on the space of formal bivectors does not accumulate at 0 too quickly.