Blowup for flat slow manifolds

In this paper we present a method for extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimension, they do appear naturally in certain settings. For example in (a) the regularization of piecewise smooth systems by $\tanh$, (b) a model of aircraft landing dynamics, and finally (c) in a model of earthquake faulting. We demonstrate the approach on a simple model system and the examples (a) and (b).