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Transseries and real differential algebra / J. van der Hoeven.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1888.Publication details: Berlin : Springer, 2006.Description: 1 online resource (xii, 255 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540355915
  • 354035591X
  • 3540355901
  • 9783540355908
  • 661070029X
  • 9786610700295
Subject(s): Genre/Form: Additional physical formats: Print version:: Transseries and real differential algebra.DDC classification:
  • 512.56 22
LOC classification:
  • QA247.4 .H64 2006eb
Other classification:
  • 31.44
  • O155
Online resources:
Contents:
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.
In: OhioLINK electronic book center In: SpringerLinkSummary: 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.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library eBook LN Mathematic Available
Total holds: 0

Includes bibliographical references (pages 235-239) and index.

Print version record.

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.

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.

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