Solution Manifolds for Systems of Differentialequationsjohn

This paper deenes a solution manifold and a stable submanifold for a system of diierential equations. Although we eventually work in the smooth topos, the rst two sections do not mention topos theory and should be of interest to non-topos theorists. The paper characterizes solutions in terms of barriers to growth and deenes solutions in what are called lter rings (characterized as C 1-reduced rings in a paper of Moerdijk and Reyes). We examine standardization, stabilization, perturbation, change of variables, non-standard solutions, strange attractors and cycles at innnity.