Normalizing Asymptotic Differential Equations

Abstract

We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization theorems for algebraic differential equations over $H$-fields, as a tool in solving such equations in suitable extensions. The results in this monograph are essential in our work on Hardy fields in [6].

176 pp.; revised based on comments by reviewers; to appear in Memoirs of the European Mathematical Society. arXiv admin note: substantial text overlap with arXiv:2304.10846