Local analytic classification of q-difference equations

2009/03/04 by Ramis, J. -P., Sauloy, J., Zhang, C.
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0903.0853

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.

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