Analytic linearization of nonlinear perturbations of Fuchsian systems

Details Analytic linearization of nonlinear perturbations of Fuchsian systems Analytic linearization of nonlinear perturbations of Fuchsian systems

2007-06-15

arxiv.org/abs/0706.2348v2

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1088/0951-7715/21/9/010

Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the case when the linear part has commuting monodromy, and the eigenvalues have positive real parts, there exists a unique correction function of the nonlinear part so that the corrected system becomes analytically linearizable.

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