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- W3099681807 abstract "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 deg q and ord q define two valuations on 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 also consider 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." @default.
- W3099681807 created "2020-11-23" @default.
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- W3099681807 date "2008-03-21" @default.
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- W3099681807 title "An ultrametric version of the Maillet-Malgrange theorem for nonlinear $q$-difference equations" @default.
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- W3099681807 doi "https://doi.org/10.1090/s0002-9939-08-09352-0" @default.
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