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Displaying similar documents to “Bi-Hamiltonian structure as a shadow of non-Noether symmetry.”

Andrew Lenard: a mystery unraveled.

Praught, Jeffery, Smirnov, Roman G. (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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A simple proof of the non-integrability of the first and the second Painlevé equations

Henryk Żołądek (2011)

Banach Center Publications

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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.