A Work on the Degree of Generality Revealed in the Organization of Enumerations: Poincaré’s Classification of Singular Points of Differential Equations

2015 ◽  
pp. 385-419
Author(s):  
Anne Robadey
Keyword(s):  
Differential Equations ◽  
Singular Points

scholarly journals ON THE CLASSIFICATION OF SINGULAR AUTOMORPHIC DIFFERENTIAL EQUATIONS AND FLOW S ON THE RIEMANN SPHERE

1995 ◽  
Vol 26 (1) ◽  
pp. 13-19
Author(s):  
K. F. KUIKEN ◽  
J. T. MASTERSON
Keyword(s):  
Differential Equations ◽  
Riemann Sphere ◽  
Fluid Flows ◽  
Second Order ◽  
Singular Points ◽  
Conic Sections ◽  
Countable Number ◽  
Second Order Differential Equations

In this paper, parameterizations are constructed for spaces of automor­ phic second order differential equations on certam subsets of $\hat C$. These equations have coefficients with a countable number of regular singular points on fundamen­ tal domains for bimeromorphic deformations of Kleiman groups. The equations considered are generalizations of classically-considered equations, including the hy­ pergeometric and Heun's equations, or have singular points on fam1hes of curves, including lines, conic sections, Joukowski airfoils or biconformal images of these curves. Global fluid flows associate with these equations are constructed and classified.

scholarly journals Limit Behavior of Solutions of Ordinary Linear Differential Equations

1994 ◽  
Vol 1 (3) ◽  
pp. 315-323
Author(s):  
František Neuman
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Linear Differential Equations ◽  
Limit Behavior ◽  
Limit Sets ◽  
Equivalent Linear ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations

Abstract A classification of classes of equivalent linear differential equations with respect to ω-limit sets of their canonical representatives is introduced. Some consequences of this classification to the oscillatory behavior of solution spaces are presented.

scholarly journals LOCAL MONODROMY OF p-ADIC DIFFERENTIAL EQUATIONS: AN OVERVIEW

2005 ◽  
Vol 01 (01) ◽  
pp. 109-154 ◽  
Author(s):  
KIRAN S. KEDLAYA
Keyword(s):  
Differential Equations ◽  
Local Monodromy ◽  
Expository Article

This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda's classification of quasi-unipotent ∇-modules, the Christol–Mebkhout construction of the ramification filtration, and the Christol–Dwork Frobenius antecedent theorem. We also briefly discuss the p-adic local monodromy theorem without proof.

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