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Coordinate transformations for singular perturbation problem. (English) Zbl 0837.34062

Singular perturbation methods are reformulated with the aid of Lie’s invariant transformation group. Singularities are analyzed through the expansion in a small parameter and in order to modify the singularity new independent variables are introduced as the canonical coordinates for the projectable group. Several examples of the algebraic and the differential equations are shown.

MSC:

34E15 Singular perturbations for ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34D15 Singular perturbations of ordinary differential equations
58D19 Group actions and symmetry properties
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