2021
DOI: 10.48550/arxiv.2109.02107
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Normal Forms of second order Ordinary Differential Equations $y_{xx}=J(x,y,y_{x})$ under Fibre-Preserving Maps

Abstract: We study the equivalence problem of classifying second order ordinary differential equations y xx = J(x, y, y x ) modulo fibre-preserving point transformations x −→ ϕ(x), y −→ ψ(x, y) by using Moser's method of normal forms. We first compute a basis of the Lie algebra g {yxx=0} of fibre-preserving symmetries of y xx = 0. In the formal theory of Moser's method, this Lie algebra is used to give an explicit description of the set of normal forms N , and we show that the set is an ideal in the space of formal powe… Show more

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