Asymptotic Differential Algebra and Model Theory of Transseries : : (AMS-195) / / Matthias Aschenbrenner, Joris van der Hoeven, Lou van den Dries.
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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| Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 |
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| VerfasserIn: | |
| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2017] ©2017 |
| Rok wydania: | 2017 |
| Język: | English |
| Seria: | Annals of Mathematics Studies ;
195 |
| Dostęp online: | |
| Opis fizyczny: | 1 online resource (880 p.) :; 12 line illus. |
| Etykiety: |
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| LEADER | 09507nam a22019815i 4500 | ||
|---|---|---|---|
| 001 | 9781400885411 | ||
| 003 | DE-B1597 | ||
| 005 | 20220131112047.0 | ||
| 006 | m|||||o||d|||||||| | ||
| 007 | cr || |||||||| | ||
| 008 | 220131t20172017nju fo d z eng d | ||
| 019 | |a (OCoLC)986538411 | ||
| 020 | |a 9781400885411 | ||
| 024 | 7 | |a 10.1515/9781400885411 |2 doi | |
| 035 | |a (DE-B1597)477787 | ||
| 035 | |a (OCoLC)984643717 | ||
| 040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
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| 044 | |a nju |c US-NJ | ||
| 050 | 4 | |a QA295 |b .A87 2017eb | |
| 072 | 7 | |a MAT002010 |2 bisacsh | |
| 082 | 0 | 4 | |a 512/.56 |2 23 |
| 084 | |a SI 830 |2 rvk |0 (DE-625)rvk/143195: | ||
| 100 | 1 | |a Aschenbrenner, Matthias, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Asymptotic Differential Algebra and Model Theory of Transseries : |b (AMS-195) / |c Matthias Aschenbrenner, Joris van der Hoeven, Lou van den Dries. |
| 264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2017] | |
| 264 | 4 | |c ©2017 | |
| 300 | |a 1 online resource (880 p.) : |b 12 line illus. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a Annals of Mathematics Studies ; |v 195 | |
| 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 |
| 506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
| 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. | ||
| 530 | |a Issued also in print. | ||
| 538 | |a Mode of access: Internet via World Wide Web. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
| 650 | 0 | |a Asymptotic expansions. | |
| 650 | 0 | |a Differential algebra. | |
| 650 | 0 | |a Divergent series. | |
| 650 | 0 | |a Series, Arithmetic. | |
| 650 | 7 | |a MATHEMATICS / Algebra / Abstract. |2 bisacsh | |
| 653 | |a Equalizer Theorem. | ||
| 653 | |a H-asymptotic couple. | ||
| 653 | |a H-asymptotic field. | ||
| 653 | |a H-field. | ||
| 653 | |a Hahn Embedding Theorem. | ||
| 653 | |a Hahn space. | ||
| 653 | |a Johnson's Theorem. | ||
| 653 | |a Krull's Principal Ideal Theorem. | ||
| 653 | |a Kähler differentials. | ||
| 653 | |a Liouville closed H-field. | ||
| 653 | |a Liouville closure. | ||
| 653 | |a Newton degree. | ||
| 653 | |a Newton diagram. | ||
| 653 | |a Newton multiplicity. | ||
| 653 | |a Newton tree. | ||
| 653 | |a Newton weight. | ||
| 653 | |a Newton-Liouville closure. | ||
| 653 | |a Riccati transform. | ||
| 653 | |a Scanlon's extension. | ||
| 653 | |a Zariski topology. | ||
| 653 | |a algebraic differential equation. | ||
| 653 | |a algebraic extension. | ||
| 653 | |a angular component map. | ||
| 653 | |a asymptotic couple. | ||
| 653 | |a asymptotic differential algebra. | ||
| 653 | |a asymptotic field. | ||
| 653 | |a asymptotic relation. | ||
| 653 | |a asymptotics. | ||
| 653 | |a closed H-asymptotic couple. | ||
| 653 | |a closure properties. | ||
| 653 | |a coarsening. | ||
| 653 | |a commutative algebra. | ||
| 653 | |a commutative ring. | ||
| 653 | |a compositional conjugation. | ||
| 653 | |a constant. | ||
| 653 | |a continuity. | ||
| 653 | |a d-henselian. | ||
| 653 | |a d-henselianity. | ||
| 653 | |a decomposition. | ||
| 653 | |a derivation. | ||
| 653 | |a differential field extension. | ||
| 653 | |a differential field. | ||
| 653 | |a differential module. | ||
| 653 | |a differential polynomial. | ||
| 653 | |a differential-hensel. | ||
| 653 | |a differential-henselian field. | ||
| 653 | |a differential-henselianity. | ||
| 653 | |a differential-valued extension. | ||
| 653 | |a differentially closed field. | ||
| 653 | |a dominant part. | ||
| 653 | |a equivalence. | ||
| 653 | |a eventual quantities. | ||
| 653 | |a exponential integral. | ||
| 653 | |a extension. | ||
| 653 | |a filtered module. | ||
| 653 | |a gaussian extension. | ||
| 653 | |a grid-based transseries. | ||
| 653 | |a henselian valued field. | ||
| 653 | |a homogeneous differential polynomial. | ||
| 653 | |a immediate extension. | ||
| 653 | |a integral. | ||
| 653 | |a integrally closed domain. | ||
| 653 | |a linear differential equation. | ||
| 653 | |a linear differential operator. | ||
| 653 | |a linear differential polynomial. | ||
| 653 | |a mathematics. | ||
| 653 | |a maximal immediate extension. | ||
| 653 | |a model companion. | ||
| 653 | |a monotonicity. | ||
| 653 | |a noetherian ring. | ||
| 653 | |a ordered abelian group. | ||
| 653 | |a ordered differential field. | ||
| 653 | |a ordered set. | ||
| 653 | |a pre-differential-valued field. | ||
| 653 | |a pseudocauchy sequence. | ||
| 653 | |a pseudoconvergence. | ||
| 653 | |a quantifier elimination. | ||
| 653 | |a rational asymptotic integration. | ||
| 653 | |a regular local ring. | ||
| 653 | |a residue field. | ||
| 653 | |a simple differential ring. | ||
| 653 | |a small derivation. | ||
| 653 | |a special cut. | ||
| 653 | |a specialization. | ||
| 653 | |a substructure. | ||
| 653 | |a transseries. | ||
| 653 | |a triangular automorphism. | ||
| 653 | |a triangular derivation. | ||
| 653 | |a valuation topology. | ||
| 653 | |a valuation. | ||
| 653 | |a value group. | ||
| 653 | |a valued abelian group. | ||
| 653 | |a valued differential field. | ||
| 653 | |a valued field. | ||
| 653 | |a valued vector space. | ||
| 700 | 1 | |a van den Dries, Lou, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a van der Hoeven, Joris, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2017 |z 9783110540550 |o ZDB-23-DGG |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2017 |z 9783110548204 |o ZDB-23-DMA |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press Complete eBook-Package 2017 |z 9783110543322 |
| 776 | 0 | |c print |z 9780691175430 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400885411?locatt=mode:legacy |
| 856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400885411 |
| 856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400885411/original |
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