ON QUASIPERIODIC SOLUTIONS OF THE MATRIX RICCATI EQUATION
V. S. Pron'kin · Izvestiya Mathematics · 1994
The matrix Riccati equation (*)is considered, where is an unknown vector, is a constant diagonal matrix whose elements are pairwise distinct imaginary numbers, the coefficients , , and are matrices whose elements are Arnold'd functions, and is a small complex parameter. Newton's method is used to prove that (*) has quasiperiodic solutions with the exception of finitely many rays. By using the quasiperiodic solutions obtained it is proved that, with the exception of finitely many rays, the system of differential equations is reducible, where is a matrix whose elements are Arnol'd functions, and is a small complex parameter.