2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75473This 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 pointSpectral TheoryAnalysis of PDEs31C10; 35P20; 35Q40; 37J35; 37J45; 53D22; 58J40Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions IIIa. One branching pointtext