Order one equations with the Painlevé property

Details Order one equations with the Painlevé property Order one equations with the Painlevé property

2012-02-21

arxiv.org/abs/1202.4633v1

G. Muntingh, M. van der Put. Order One Equations with the Painlev\'e Property. Indagationes Mathematicae, N.S., 18 (1), 2007,

Mathematics

Algebraic Geometry

1 figure

Scientific paper

10.1016/S0019-3577(07)80009-7

Differential equations with the Painlev\'e property have been studied extensively due to their appearance in many branches of mathematics and their applicability in physics. Although a modern, differential algebraic treatment of the order one equations appeared before, the connection with the classical theory did not. Using techniques from algebraic geometry we provide the link between the classical and the modern treatment, and with the help of differential Galois theory a new classification is derived, both for characteristic 0 and p.

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