We study the stability of singular points for smooth Poisson structures as
well as general Lie algebroids. We give sufficient conditions for stability
lying on the first (not necessarily linear) approximation of the given Poisson
structure or Lie algebroid at a singular point. The main tools used here are
the classical Lichnerowicz-Poisson cohomology and the deformation cohomology
for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide
several examples of stable singular points of order kâ„1 for Poisson
structures and Lie algebroids. Finally, we apply our results to pre-symplectic
leaves of Dirac manifolds.Comment: corrected typo