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Kovalevska vs. Kovacic-two different notions of integrability and their connections

Paweł Goldstein — 2002

Banach Center Publications

Ordinary differential equations all share the same common root-real physical problems. But, although the physical motivation remains the most important one, the way the subject develops does depend highly on the methods available. In the exposition I would like to show some connections between two methods of checking the ODE for integrability (whatever it should mean), with distant motivations and techniques. These are the so-called Painlevé tests and the methods originating in Ziglin's theory and...

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