Non-Fuchsian extension to the Painlev\'e test
classification
solv-int
nlin.SI
keywords
equationfuchsianmovablenon-fuchsiannonlinearpainlevtestconsider
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We consider meromorphic particular solutions of nonlinear ordinary differential equations and perform a perturbation {\it \`a la} Poincar\'e 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) Painlev\'e test.
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