English

Local analytic classification of q-difference equations

Quantum Algebra 2012-01-31 v3

Abstract

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-Guenter normal forms, q-analogues of the so-called Birkhoff-Malgrange-Sibuya theorems and a new theory of summation. The results were announced in [C. R. Math. Acad. Sci.] and in various seminars and conferences between 2004 and 2006.

Keywords

Cite

@article{arxiv.0903.0853,
  title  = {Local analytic classification of q-difference equations},
  author = {J. -P. Ramis and J. Sauloy and C. Zhang},
  journal= {arXiv preprint arXiv:0903.0853},
  year   = {2012}
}

Comments

176 pages

R2 v1 2026-06-21T12:18:26.390Z