Transseries and Real Differential Algebra
Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equatio
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Lecture Notes in Mathematics
1
Joris van der Hoeven
Transseries and Real Differential Algebra
1888
1 23
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1888
J. van der Hoeven
Transseries and Real Differential Algebra
ABC
Author Joris van der Hoeven Département de Mathématiques, CNRS Université Paris-Sud Bâtiment 425 91405 Orsay CX France e-mail: [email protected]
Library of Congress Control Number: 2006930997 Mathematics Subject Classification (2000): 34E13, 03C65, 68w30, 34M35, 13H05 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-35590-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-35590-8 Springer Berlin Heidelberg New York DOI 10.1007/3-540-35590-1
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SPIN: 11771975
VA41/3100/SPi
543210
Table of Contents
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
XI
Introduction . . . . . . . . . The field with no escape Historical perspectives . Outline of the contents Notations . . . . . . . . .
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Orderings . . . . . . . . . . 1.1 Quasi-orderings . . . . 1.2 Ordinal numbers . . . 1.3 Well-quasi-orderings . 1.4 Kruskal’s theorem . . 1.5 Ordered structures . . 1.6 Asymptotic relations 1.7 Hahn spaces . . . . . . 1.8 Groups and rings with
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