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Asymptotic Differential Algebra and Model Theory of Transseries
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Asymptotic Differential Algebra and Model Theory of Transseries

Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

Abstract

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suita ... More

Keywords: asymptotic differential algebra, differential field, asymptotics, transseries, differential-hensel, H-field, Newton–Liouville closure, valuation, valued differential field

Bibliographic Information

Print publication date: 2017 Print ISBN-13: 9780691175423
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691175423.001.0001

Authors

Affiliations are at time of print publication.

Matthias Aschenbrenner, author
University of California, Los Angeles

Lou van den Dries, author
University of Illinois

Joris van der Hoeven, author
Ecole Polytechnique