Non-Fuchsian extension to the Painlevé test

Micheline Musette; Robert Conte

doi:10.1016/0375-9601(95)00602-y

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Non-Fuchsian extension to the Painlevé test

Micheline Musette·Robert Conte

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Abstract

We consider meromorphic particular solutions of nonlinear ordinary differential equations and perform a perturbation {\it à la} Poincaré making their linearized equation non-Fuchsian at the movable pole and Fuchsian at infinity. When the nonlinear equation possesses movable logarithms, they are detected sooner than with the perturbative (Fuchsian) Painlevé test.

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Micheline Musette, Robert Conte. 1995-08-28. Non-Fuchsian extension to the Painlevé test. https://doi.org/10.1016/0375-9601(95)00602-y

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