(Université de Limoges, Laboratoire XLIM (CNRS UMR (72 52))
Fecha, hora y lugar: Martes 5 de mayo de 2015 a las 17:00 en la sala 125 de la Facultad de Ciencias de Valladolid.
Título:On Apparent Singularities of Systems of Linear Differential
Equations with Rational Function Coefficients
Resumen: Let (S) $Y' = A(x)Y$ be a system of first order linear differential equations with rational function coefficients. The (finite) singularities of (S) are the poles of the entries de the matrix $A(x)$. A singular point $x_0$ of (S) is called an apparent singularity for $(S)$ if there is a basis of solutions of (S) which are holomorphic in a neighborhood of $x_0$. In this talk we shall present a new algorithm which, given a system of the form (S), detects apparent singularities and constructs an equivalent system (S') with rational coefficients the singularities of which coincide with the non apparent singularities of (S). Our method can, in particular, be applied to the companion system of any linear differential equation with arbitrary order $n$ . We thus have an alternative method to the standard methods for removing apparent singularities of linear differential operators. We shall compare our method to the one designed for operators and we shall show some applications and examples of computation.