Since 1999, every report released by the International Panel on Climate Change has advocated a decrease in the greenhouse gas emissions associated with aviation in order to preserve the current climate. This study used a two variable differential equations model with a non-linear control term to address several aspects of the emissions stabilization issue. By optimizing the control term parameter, several management alternatives can be obtained based on the properties of the phase plane of the model solutions, as identified by a stability analysis. The system can be stabilised around an equilibrium point that maintains the present number of passengers, or maintains the emissions level or is nearest to its present state. Each of these options entails different issues of growth or reduction in the number of passengers and/or the emissions rate, directly obtained from the model results. The last option seems especially novel and promising, since only short-distance flight passengers are severely reduced, while long-distance and international passengers are allowed to growth, and their associated emissions are reduced to below 50 percent of their actual value. Moreover, in a scenario of slow growth in air traffic, these rates could improve, with fewer reductions in the number of short-distance passengers.