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

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

2007-06-15

arxiv.org/abs/0706.2343v2

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1088/0951-7715/21/9/009

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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