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

Published online by Cambridge University Press:  17 February 2009

Gerhard Jank
Gerhard Jank
Affiliation:
Lehrstuhl II für Mathematik, RWTH Aachen, Templergraben 55, D-5100 Aachen, Federal Republic of, Germany.
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Abstract

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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 co-efficients 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 certain domains around the permanent critical directions, in a circle of radius r, is of growth O(log r). Applications of the results to periodic solutions and to the determination of critical points are given.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 1 , July 1992 , pp. 112 - 131
Copyright
Copyright © Australian Mathematical Society 1992

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