Stability theory

Abstract

In this chapter we present an introduction to the theory of stability. Since this is a very broad area which includes not only many topics but also various notions of stability, we mainly focus on Liapunov stability of equilibrium points and leave out topics such as the Poincaré–Bendixon theory, stability of periodic solutions, limit cycles, etc. Some of the proofs are omitted or carried out in special simple cases. For a more complete treatment the reader may consult sources such as the books by J. La Salle & S. Lefschetz, or by H. Amann, see Bibliography.