BIRKHOFF REDUCTION OF TWO-DIMENSIONAL LINEAR DIFFERENTIAL SYSTEMS AT A SINGULAR POINT.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Two-dimensional systems of linear differential equations are considered in a neighborhood of a pole of the coefficient matrix. A linear transformation is applied to the system which simplifies the expansion of the coefficient matrix which is then said to be in a modified Birkhoff canonical form. Solutions of the transformed system are equivalent to those of the original system in the sense that they display common singular behavior in a neighborhood of the pole. Some information about the solutions can be read directly from the canonical form. Author
- Theoretical Mathematics