An ultrametric version of the Maillet-Malgrange theorem for nonlinear q-difference equations
| dc.creator | Di Vizio, Lucia | |
| dc.date | 2007-09-16 | |
| dc.date | 2008-03-18 | |
| dc.date.accessioned | 2026-07-07T09:35:42Z | |
| dc.date.available | 2026-07-07T09:35:42Z | |
| dc.description | We prove an ultrametric q-difference version of the Maillet-Malgrange theorem, on the Gevrey nature of formal solutions of nonlinear analytic q-difference equations. Since °_q and \ord_q define two valuations on {\mathbb C}(q), we obtain, in particular, a result on the growth of the degree in q and the order at q of formal solutions of nonlinear q-difference equations, when q is a parameter. We illustrate the main theorem by considering two examples: a q-deformation of ``Painleve' II'', for the nonlinear situation, and a q-difference equation satisfied by the colored Jones polynomials of the figure 8 knots, in the linear case. We consider also a q-analog of the Maillet-Malgrange theorem, both in the complex and in the ultrametric setting, under the assumption that |q|=1 and a classical diophantine condition. | |
| dc.description | 11 pages; many language inaccuracies have been corrected | |
| dc.identifier | https://arxiv.org/abs/0709.2464 | |
| dc.identifier | http://arxiv.org/abs/0709.2464 | |
| dc.identifier | Proc. Amer. Math. Soc. 136 (2008), 2803-2814. | |
| dc.identifier | doi:10.1090/S0002-9939-08-09352-0 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159917 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Number Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 33E99, 39A13 | |
| dc.title | An ultrametric version of the Maillet-Malgrange theorem for nonlinear q-difference equations | |
| dc.type | text |