The Eighteenth Week: Regular Singularities

Michio Kuga

A chapter in Galois’ Dream: Group Theory and Differential Equations, 1993, pp 114-128 from Springer

Abstract: Abstract First, let us review some basic facts about differential equations with regular singularities. (For details, see Birkhoff-Rota [4], for example.) Consider an open disc U = U(a; ε)of radius ε and center a in the complex plane C. Let Ua denote U - {a}. We call such a region a “5-yen coin.” Choose a point b in U a and let z : $$\left( {{{\tilde U}_a},\tilde b} \right) \to \left( {{U_a},b} \right)$$ be the universal covering. We call Ũ a a spiral staircase. For simplicity, we assume that b - a is a positive real number.

Keywords: Universal Covering; Laurent Expansion; Jordan Form; Convergent Power Series; Regular Singularity (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0329-2_19

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DOI: 10.1007/978-1-4612-0329-2_19

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