Cooperation of orbital streams in disc galaxies

An orbit is said to cooperate with a potential well if it tends to deepen it by aligning with it. We derive analytical formulae that give the response of resonant orbits to nonaxisymmetric perturbations. This makes it possible to quantify the level of cooperation in a given galaxy model. The qualitative response of orbits can be characterized by the sign of what we call the cooperation parameter. We discuss the relevance of our results for theories of the formation and maintenance of bars and lopsidedness.