Levi decomposition for smooth Poisson structures
  We prove the existence of a local smooth Levi decomposition for smooth Poisson structures and Lie algebroids near a singular point. In the appendix of this paper, we show an abstract Nash-Moser normal form theorem, which generalizes our Levi decomposition result and which may be helpful in the study of other smooth normal form problems. 
Philippe Monnier and Nguyen Tien Zung