Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions   IIIa. One branching point
  This is the third in a series of works devoted to spectral asymptotics for non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. We assume that the unperturbed operator has a periodic Hamilton flow, and study the remaining generic case; when the flow average of the perturbation has a saddle point 
M. Hitrik, J. Sjoestrand