Power Series Solutions of Non-Linear q-Difference Equations and the Newton-Puiseux Polygon

Jos\'e Cano; Pedro Fortuny Ayuso

Power Series Solutions of Non-Linear q-Difference Equations and the Newton-Puiseux Polygon

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arxiv 1209.0295 v2 pith:FD66ALV5 submitted 2012-09-03 math.AG

José Cano , Pedro Fortuny Ayuso This is my paper · ORCID

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keywords ordersolutionsequationsnewton-puiseuxpolygonpowerq-differenceseries

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abstract

Adapting the Newton-Puiseux Polygon process to nonlinear q-difference equations of any order and degree, we compute their power series solutions, study the properties of the set of exponents of the solutions and give a bound for their $q-$Gevrey order in terms of the order of the original equation.

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Polygons of Petrovic and Fine, algebraic ODEs, and contemporary mathematics
math.CA 2019-08 conditional novelty 4.0 of 10

A historical and mathematical study showing that Petrovic's and Fine's 1890s polygon methods generalize Newton-Puiseux theory and anticipate modern power geometry.

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