Asymptotic Differential Algebra and Model Theory of Transseries (Paperback)

Idioma: inglés

Editorial: Princeton University Press, New Jersey, 2017

0691175438 / 9780691175430

Serie: Libro 187 de 202 - Annals of Mathematics Studies

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Paperback. 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 suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity.Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences. 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, transser Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

N° de ref. del artículo 9780691175430

Título
Asymptotic Differential Algebra and Model Theory of Transseries (Paperback)
Autor
Matthias Aschenbrenner
Editorial
Princeton University Press, New Jersey
Año de publicación
2017
Estado
new
Encuadernación
Paperback
Idioma
inglés
ISBN 10
0691175438
ISBN 13
9780691175430
Serie
Libro 187 de 202: Annals of Mathematics Studies

Grand Eagle Retail

Bensenville, IL, Estados Unidos de America

Vendedor de 5 estrellas

Vendedor de IberLibro desde 12 de octubre de 2005

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