Ramani, A.; Grammaticos, B.; Tremblay, S. Integrable systems without the Painlevé property. (English) Zbl 0953.34077 J. Phys. A, Math. Gen. 33, No. 15, 3045-3052 (2000). 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. Cited in 12 Documents 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 Keywords:Painlevé property; nonlinear ordinary differential equations PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 33, No. 15, 3045--3052 (2000; Zbl 0953.34077) Full Text: DOI arXiv