Local analytic classification of q-difference equations
By: Jean-Pierre Ramis, Jacques Sauloy, Changgui Zhang
Contributors: Sauloy, Jacques, author; Zhang, Changgui, 1966- author
Series: Astérisque -- 355; Astérisque -- 355.
Publisher: Société mathématique de France
Published: 2013
Place of publication: Paris
Language: eng
Number of pages: 151
ISBN-13: 9782856297759
Copyright date: 2013
Subjects: Difference equations; Riemann-Hilbert problems
Description: 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.
Notes: Includes bibliographical references (pages 139-143) and indexes.

Text in English; abstract in both English and French.
Table of contents: title: Introduction; title: Some general nonsense; title: The affine space of isoformal analytic classes; title: The q-analogs of Birkhoff-Malgrange-Sibuya theorems; title: Summation and asymptotic theory; title: Geometry of the space of classes; title: Examples of the Stokes phenomenon; title: Classification of isograded filtered difference modules.