Submission date: 2 August 2016

Abstract:

An H-field is a type of ordered valued differential field studied in asymptotic differential algebra. The main examples of H-fields include Hardy fields and fields of transseries. We study here λ-freedom, a property of H-fields that prevents certain undesirable deviant behavior. In particular, we show that under certain types of extensions related to adjoining integrals and exponential integrals, the property of λ-freedom is preserved. Much of our analysis is done in the more general setting of differential-valued fields, where a field ordering might not present. The main application of our work is a complete characterization of exactly when an H-field has one or two Liouville closures, closing a gap in [MZ].

Mathematics Subject Classification:

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Full text arXiv 1608.00997: pdf, ps.