Crainic, M.; Fernandes, R.L.; Algebra & Geometry and Mathematical Locic; Analysis; Sub Algebra,Geometry&Mathem. Logic begr.
We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not only extends but also provides a new approach (and proofs) to the classical stability results for foliations and group actions.