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Local analytic classification of q-difference equations / Jean-Pierre Ramis, Jacques Sauloy and Changgui Zhang.

By: Contributor(s): Material type: TextTextSeries: Asterisque ; 355.Publication details: Paris : Societe mathematique de France, 2013.Description: vi, 151 p. : illustrations ; 24 cmISBN:
  • 9782856297759 (paperback)
Subject(s): DDC classification:
  • 510=4 23 As853
Contents:
1. Introduction -- 2. Some general nonsense -- 3. The affine space of isoformal analytic classes -- 4. The q-analogs of Birkhoff-Malgrange-Sibuya theorems -- 5. Summation and asymptotic theory -- 6. Geometry of the space of classes -- 7. Examples of the Stokes phenomenon -- A. Classification of isograded filtered difference modules-- Bibliography-- Index of notations-- Index.
Summary: We essentially achieve Birkhoff's program for q-difference equations by giving three different descriptions of the moduli space of isoformal analytic classes. This involves an extension of Birkhoff-Guenther normal forms, q-analogues of the so-called Birkhoff-Malgrange--Sibuya theorems and a new theory of summation. The results were announced in various seminars and conferences between 2004 and 2006.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510=4 As853 (Browse shelf(Opens below)) Available C26461
Total holds: 0

Includes bibliographical references (pages 139-143) and indexes.

1. Introduction --
2. Some general nonsense --
3. The affine space of isoformal analytic classes --
4. The q-analogs of Birkhoff-Malgrange-Sibuya theorems --
5. Summation and asymptotic theory --
6. Geometry of the space of classes --
7. Examples of the Stokes phenomenon --
A. Classification of isograded filtered difference modules--
Bibliography--
Index of notations--
Index.

We essentially achieve Birkhoff's program for q-difference equations by giving three different descriptions of the moduli space of isoformal analytic classes. This involves an extension of Birkhoff-Guenther normal forms, q-analogues of the so-called Birkhoff-Malgrange--Sibuya theorems and a new theory of summation. The results were announced in various seminars and conferences between 2004 and 2006.

Text in English; abstract in both English and French.

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