Local analytic classification of q-difference equations

Details Local analytic classification of q-difference equations Local analytic classification of q-difference equations

2009-03-04

arxiv.org/abs/0903.0853v3

Mathematics

Quantum Algebra

176 pages

Scientific paper

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.

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