TY  - BOOK
AU  - Hoeven,J.van der
TI  - Transseries and real differential algebra
T2  - Lecture notes in mathematics,
SN  - 9783540355915
AV  - QA247.4 .H64 2006eb
U1  - 512.56 22
PY  - 2006///
CY  - Berlin
PB  - Springer
KW  - Differential algebra
KW  - Series, Arithmetic
KW  - Algèbre différentielle
KW  - Séries arithmétiques
KW  - arithmetic progressions
KW  - aat
KW  - MATHEMATICS
KW  - Algebra
KW  - Linear
KW  - bisacsh
KW  - cct
KW  - Álgebra diferencial
KW  - embucm
KW  - fast
KW  - Differentiaalrekening
KW  - gtt
KW  - Academic Dissertation
KW  - dissertations
KW  - Academic theses
KW  - lcgft
KW  - Thèses et écrits académiques
KW  - rvmgf
N1  - Includes bibliographical references (pages 235-239) and index; Orderings -- Grdi-based series -- The Newton polygon method -- Transseries -- Operations on transseries -- Grid-based operators -- Linear differential equations -- Algebraic differential equations -- The intermediate value theorem; University staff and students only. Requires University Computer Account login off-campus
N2  - 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 equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/3-540-35590-1
ER  -