ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

Frequently, the evolution of real phenomena is described by systems of ordinary differential equations. These systems express physical laws, geometrical connections, and they are often obtained by neglecting some influences and quantities which are assumed negligible with respect to others. The simplified system describes correctly the real phenomenon if and only if it is topologically equivalent to the system in which the small influences and quantities are also included. This means that there exists a homeomorphism of the parameter space and a parameter dependent homeomorphism of the phase-space, which sends the orbits of the simplified system onto the orbits of the non simplified system. A system defined in a region D is structurally stable in a sub-region of D if any system sufficiently close in D is topologically equivalent in the sub-region to the initial system. This talk presents systems used in aerospace engineering which are structurally stable, systems for which structural stability has never been proved, and systems which are not structurally stable, opening the problem of legitimacy of the use of the last two types of systems.