Asymptotic distribution of singularities of solutions of Matrix-Riccati differential equations

Gerhard Jank
1992 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
In the present paper, we make use of the method of asymptotic integration to get estimates on those regions in the complex plane where singularities and critical points of solutions of the Matrix-Riccati differential equation with polynomial coefficients may appear. The result is that most of these points lie around a finite number of permanent critical directions. These permanent directions are defined by the coefficients of the differential equation. The number of singularities outside
more » ... ties outside certain domains around the permanent critical directions, in a circle of radius r , is of growth 0(log r). Applications of the results to periodic solutions and to the determination of critical points are given.
doi:10.1017/s0334270000007402 fatcat:jxykqlkjhnbopjvrfgatdz3iue