Justification of Painlevé analysis for Hamiltonian systems by differential Galois theory

H. Yoshida

Physica A: Statistical Mechanics and its Applications, 2000, vol. 288, issue 1, 424-430

Abstract: The discovery of the Kowalevski top (1889) as a new integrable system posed the question whether there exists a rigorous relation between integrability of a Hamiltonian system and the analytic property of the solution in the complex time plane. Many examples suggest a hidden relation between the nature of singularities of solution, and the integrability of the system. Without enough justification of the method itself, this so-called Painlevé analysis (to determine the values of parameters such that the singularities are only poles) made it possible to discover some new integrable systems. In this paper, a recent justification of this analysis will be reviewed which is based on the differential Galois theory. A rigorous statement is that possessing the weak Painlevé property is a necessary condition for integrability of Hamiltonian systems with a homogeneous potential.

Keywords: Integrability; Non-integrability; Differential Galois theory; Painlevé analysis (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:288:y:2000:i:1:p:424-430

DOI: 10.1016/S0378-4371(00)00440-4

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