About fractional-linear system of an order 2 <i>n</i>, which solutions not contain movable multi-valued singularities
The object of this research is a nonlinear system of two differential equations with fractional-linear right-hand sides, each of which has an order <i>n</i>. The purpose of the research is to find necessary and sufficient conditions of an absence of movable multi-valued singularities of the considered system solutions. In the major part an author considers, that with a certain relation for the system coefficients using a linear change of the dependent variable we can assume that free terms of the denominators are zero. The method of Painlevé small parameter and the method of comparison of the equations we’ve got for the components of the system and equations, which analytical properties of the solutions are known, were used to find necessary and sufficient conditions for the absence of movable multi-valued singularities of the system solutions. The results can be used in the analytic theory of ordinary differential equations.