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Integrable systems without the Painlevé property. (English) Zbl 0953.34077

Summary: The authors examine whether the Painlevé property is a necessary condition for the integrability of nonlinear ordinary differential equations. They show that for a large class of linearizable systems this is not the case. In the discrete domain, they investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlevé continuous linearizable systems. They find that while these discrete systems are themselves linearizable, they possess nonconfined singularities.

MSC:

34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
39A12 Discrete version of topics in analysis
34A34 Nonlinear ordinary differential equations and systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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