Topological Obstructions

Abstract

Given the previous chapters on topology and dynamical system theory, we can now provide a consistent treatment of topological obstructions to stability and stabilization. In particular, we will see how the retraction theory from Sect. 2.2 and the index results due to Bobylev, Krasnosel’skiĭ and Zabreĭko from Sect. 3.5 cover most of the existing results, conceptually. The current chapter focuses on the obstructions themselves and the next chapter highlights potential solutions.