## Asymptotic Analysis of Solutions of Almost Diagonal Systems of Ordinary Linear Differential Equations at a Turning Point |

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### Contents

Formulation of the Problem | 6 |

A Particular Formal Series Solution | 11 |

On the Behavior of Certain Integrals | 14 |

6 other sections not shown

### Common terms and phrases

admits an asymptotic analytic proof antecedent arg cr ASYMPTOTIC ANALYSIS asymptotic character described asymptotic expansion valid asymptotic series completes the proof constant diag diagonal matrix DIAGONAL SYSTEMS differential equation DOCTOR OF PHILOSOPHY domain eigenvalues of AQ(x exists a matrix formal series solution four sectors fundamental matrix solution given equation increasing along ssQ integral equation Jordan block Jordan canonical form Jr(t known asymptotic Lemma Let the path line segment ss LINEAR DIFFERENTIAL EQUATIONS matrix P(x nilpotent nonzero number sufficiently small obtain open half plane opposite signs positive integer positive number Pr(x r=0 valid Riemann surface satisfies the following Section set A(g,x Sibuya simplified equation small number solutions of 9 straight line segment strictly increasing T-plane tA(x thesis transformation triangular region uniformly valid University of Wisconsin vector function Wasow 39 x-plane xA(x zero diagonal entries