Generalized stability theory part I: autonomous operators

Classical stability theory is extended to include growth processes. The central role of the nonnormality of the linearized dynamical system in the stability problem is emphasized, and a generalized, stability theory is constructed that is applicable to the transient as well as the asymptotic stability of time-dependent flows. Simple dynamical systems are used as examples including an illustrated nonnormal two-dimensional operator, the Eady model of baroclinic instability, and a model of convective instability in baroclinic flow.