Quasinormal modes are analogues of normal modes for physical systems in the presence of dissipation. In other words, these are the eigenstates of linearized equations of motion, e.g. of nonlinear wave equations. The eigenvalues become complex, signifying nonconservation of energy. This notion is especially prevalent recently in black hole physics.
Frederik Denef, Sean A. Hartnoll, Subir Sachdev, Black hole determinants and quasinormal modes, Class.Quant.Grav. 27, 125001 (2010), arxiv/0908.2657; Quantum oscillations and black hole ringing, Physical Review D 80, 126016 (2009), arxiv/0908.1788, journal
Shouvik Datta, Justin R. David, Higher spin quasinormal modes and one-loop determinants in the BTZ black hole, JHEP 2012:79 arxiv/1112.4619