Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms

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Abstract
Nonlinear perturbations of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions are found constructively, as a countable set of numbers. Furthermore, assuming a polynomial character of the nonlinear part, it is shown that there exists a unique formal 'correction' of the nonlinear part so that the 'corrected' system is formally linearizable. Normal forms of these systems are found, providing also their classification.

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