In axial flow compressors there are two primary modes of instability:
axisymmetric flow oscillations (surge), and asymmetric traveling wave
disturbances (rotating stall). Since the occurrence of either during normal
operation of jet aircraft engines could likely lead to catastrophic
consequences, aeroengines are typically over-designed to obviate such
Recent efforts, via active control, to suppress the instabilities and allow for more efficient designs closer to the stall/surge boundary have achieved only modest success. Difficulty arises when both modes are nearly critical, leading to complex interactions between the two types of behavior. In this talk, I present some work in progress on understanding these interactions from a dynamical systems viewpoint. In the analysis, we uncover a (quasi-) global resonant structure that can be exploited for control purposes. New challenges concerning the practical application of dynamical systems techniques to engineering systems emerge as well.