Resilience is the ability of a system to withstand and stay operational in the face of an unexpected disturbance or unpredicted changes. Recent studies on air transport system resilience focus on topology characteristics after the disturbance and measure the robustness of the network with respect to connectivity. The dynamic processes occurring at the node and link levels are often ignored. Here we analyze airport network resilience by considering both structural and dynamical aspects. We develop a simulation model to study the operational performance of the air transport system when airports operate at degraded capacity rather than completely shutting down. Our analyses show that the system deteriorates soon after disruptive events occur but returns to an acceptable level after a period of time. Static resilience of the airport network is captured by a phase transition in which a small change to airport capacity will result in a sharp change in system punctuality. After the phase transition point, decreasing airport capacity has little impact on system performance. Critical airports which have significant influence on the performance of whole system are identified, and we find that some of these cannot be detected based on the analysis of network structural indicators alone. Our work shows that air transport system's resilience can be well understood by combining network science and operational dynamics.