Kovalevska vs. Kovacic—two different notions of integrabilityand their connections
Volume 58 / 2002
Banach Center Publications 58 (2002), 63-73
MSC: Primary 34M55; Secondary 34M35
DOI: 10.4064/bc58-0-5
Abstract
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 developed widely by Morales and Ramis.
