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arXiv · 0706.2343

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

Rodica D. Costin
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Abstract

Nonlinear perturbation 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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Rodica D. Costin. 2008-07-01. Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms. https://doi.org/10.1088/0951-7715%2F21%2F9%2F009

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