Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms
Classical Analysis and ODEs
2009-11-13 v2
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.
Cite
@article{arxiv.0706.2343,
title = {Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms},
author = {Rodica D. Costin},
journal= {arXiv preprint arXiv:0706.2343},
year = {2009}
}