Both Hardy fields and fields of transseries provide interesting models of valued fields with an additional ordered differential structure. In our talk we show that the field of differentially algebraic transseries over the real numbers can be embedded in a Hardy field. The proof relies on the concept of a “transserial Hardy field”, which both carries the structure of a Hardy field and of a differential subfield of the field of transseries. We will associate analytic meanings to transseries using a technique of iterated integrals.

Occasion: Valuations 2011, Segovia, July 21–22, 2011

Documents: slideshow-1, slideshow-2, TeXmacs source