Transseries and real differential algebra /
Hoeven, J. van der
Transseries and real differential algebra / J. van der Hoeven. - Berlin : Springer, 2006. - 1 online resource (xii, 255 pages) : illustrations - Lecture notes in mathematics, 1888 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1888. .
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.
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.
9783540355915 354035591X 3540355901 9783540355908 661070029X 9786610700295
10.1007/3-540-35590-1 doi
978-3-540-35590-8 Springer http://www.springerlink.com
98074590X DE-101
Differential algebra.
Series, Arithmetic.
Algèbre différentielle.
Séries arithmétiques.
arithmetic progressions.
MATHEMATICS--Algebra--Linear.
Series, Arithmetic.
Differential algebra.
Álgebra diferencial
Differential algebra
Series, Arithmetic
Differentiaalrekening.
Academic Dissertation
dissertations.
Academic theses
Academic theses.
Thèses et écrits académiques.
QA247.4 / .H64 2006eb
512.56
Transseries and real differential algebra / J. van der Hoeven. - Berlin : Springer, 2006. - 1 online resource (xii, 255 pages) : illustrations - Lecture notes in mathematics, 1888 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1888. .
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.
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.
9783540355915 354035591X 3540355901 9783540355908 661070029X 9786610700295
10.1007/3-540-35590-1 doi
978-3-540-35590-8 Springer http://www.springerlink.com
98074590X DE-101
Differential algebra.
Series, Arithmetic.
Algèbre différentielle.
Séries arithmétiques.
arithmetic progressions.
MATHEMATICS--Algebra--Linear.
Series, Arithmetic.
Differential algebra.
Álgebra diferencial
Differential algebra
Series, Arithmetic
Differentiaalrekening.
Academic Dissertation
dissertations.
Academic theses
Academic theses.
Thèses et écrits académiques.
QA247.4 / .H64 2006eb
512.56