Topological methods

Abstract

All methods to understand multiple time scale systems we have presented so far needed some kind of mathematical analysis. In particular, for any geometric construction, asymptotic calculation, or numerical method, we needed tools such as transversality arguments, asymptotic comparison, and error estimates. But what if we are primarily interested in existence statements such as, does a given fast–slow system have a periodic orbit? In this chapter, we shall use a different approach, based on (algebraic) topology, to answer existence questions using only a minimal amount of analytic information.