Rodica D. Costin
Published 2007-06-15, updated 2008-07-01Version 2
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.
Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms
Classification of Fuchsian systems and their connection problem
Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System
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