Transseries and superexact asymptotics in ordinary and partial differential equations

Abstract

This thesis is a combination of five chapters, all related to the Theorem of Dulac. Three chapters are dedicated to a dedicated analysis of the Finiteness proof of Ilyashenko, one is about maximal totally ordered sets in real analytic functions near infinity and the final chapter is a about a generalization of some aspects of D-modules and Differential Galois Theory to modules over Hopf module algebras.