Obstruction Sets and Nonlinear Dynamics

Obstruction set is a special set defined in the phase space of a vector field, the existence of which describes some instability property of the corresponding system. The theory of obstruction-set is proposed by Shantao Liao. The theory exerts a great influence on the development of nonlinear dynamics. In this chapter first the concept of obstruction sets with the relation to stability problems is briefly introduced. Then computing formulas of obstruction sets for ordinary differential equations, in particular for two and three systems with some examples are provided. Finally, some remarkable directions of the obstruction set theory and method are discussed for the study of nonlinear dynamics.