On a “Mysterious” Case of a Quadratic Hamiltonian

Sergei Sakovich

Institute of Physics, National Academy of Sciences, 220072 Minsk, Belarus

Abstract: We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya–Lyapunov test, fails to pass the Painlevé test for integrability.

Keywords: Hamiltonian system; nonintegrability; singularity analysis.

MSC: 70H07; 37J30; 34M35

Received: June 2, 2006; in final form July 18, 2006; Published online July 28, 2006

Language: English

DOI: 10.3842/SIGMA.2006.064

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ArXiv: nlin.SI/0408027