Asymptotic Differential Algebra and Model Theory of Transseries /
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 logar...
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| Hlavní autoři: | , , |
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| Médium: | E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Princeton, NJ :
Princeton University Press,
2017
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| Edice: | Annals of Mathematics Studies ;
358 |
| Témata: | |
| ISBN: | 9781400885411 |
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| 020 | |a 9781400885411 | ||
| 024 | 7 | |a 10.1515/9781400885411 |2 doi | |
| 035 | |a CVTIDW15407 | ||
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| 041 | 0 | |a eng | |
| 044 | |a nju |c US-NJ | ||
| 080 | |a 51 |2 2011 | ||
| 080 | |a 512 |2 2011 | ||
| 100 | 1 | |a Aschenbrenner, Matthias, |4 aut. | |
| 245 | 1 | 0 | |a Asymptotic Differential Algebra and Model Theory of Transseries / |c Joris van der Hoeven, Matthias Aschenbrenner, Lou van den Dries. |
| 260 | |a Princeton, NJ : |b Princeton University Press, |c 2017 | ||
| 300 | |a 1 online resource : |b 12 line illus. | ||
| 490 | 0 | |a Annals of Mathematics Studies ; |v 358 | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Conventions and Notations -- |t Leitfaden -- |t Dramatis Personæ -- |t Introduction and Overview -- |t Chapter One. Some Commutative Algebra -- |t Chapter Two. Valued Abelian Groups -- |t Chapter Three. Valued Fields -- |t Chapter Four. Differential Polynomials -- |t Chapter Five. Linear Differential Polynomials -- |t Chapter Six. Valued Differential Fields -- |t Chapter Seven. Differential-Henselian Fields -- |t Chapter Eight. Differential-Henselian Fields with Many Constants -- |t Chapter Nine. Asymptotic Fields and Asymptotic Couples -- |t Chapter Ten. H-Fields -- |t Chapter Eleven. Eventual Quantities, Immediate Extensions, and Special Cuts -- |t Chapter Twelve. Triangular Automorphisms -- |t Chapter Thirteen. The Newton Polynomial -- |t Chapter Fourteen. Newtonian Differential Fields -- |t Chapter Fifteen. Newtonianity of Directed Unions -- |t Chapter Sixteen. Quantifier Elimination -- |t Appendix A. Transseries -- |t Appendix B. Basic Model Theory -- |t Bibliography -- |t List of Symbols -- |t Index |
| 516 | |a text file PDF | ||
| 520 | |a 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. | ||
| 650 | 7 | |a MATHEMATICS / Algebra / Abstract. |2 bisacsh | |
| 653 | |a algebra | ||
| 653 | |a matematika | ||
| 700 | 1 | |a van den Dries, Lou, |4 aut. | |
| 700 | 1 | |a van der Hoeven, Joris, |4 aut. | |
| 856 | 4 | 0 | |u http://hanproxy.cvtisr.sk/han/cvti-ebook-degruyter-isbn-9781400885411 |y Vzdialený prístup pre registrovaných používateľov |
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| 974 | |f Elektronické zdroje | ||
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