MISC

1999年4月1日

A new necessary condition for the integrability of Hamiltonian systems with a two-dimensional homogeneous potential

Physica D: Nonlinear Phenomena
  • Haruo Yoshida

128
1
開始ページ
53
終了ページ
69
記述言語
英語
掲載種別
DOI
10.1016/S0167-2789(98)00313-3
出版者・発行元
Elsevier

Recently, Morales-Ruiz and Ramis obtained a strong necessary condition for the integrability of Hamiltonian systems with a homogeneous potential based on their own theorem on the differential Galois theory (Picard-Vessiot theory) for Hamiltonian systems. The theorem claims that if the original Hamiltonian system is integrable, then the variational equation around a particular solution is solvable in the sense of the differential Galois theory, i.e., the solution is obtained only by a combination of quadratures, exponential of quadratures and algebraic functions. In this paper, a direct and independent proof of this statement is given for Hamiltonian systems with a two-dimensional homogeneous potential, which leads to the new necessary condition for integrability. This new necessary condition well justifies the so-called weak Painlevé conjecture of Ramani et al. for the first time. © 1998 Elsevier Science B.V.

リンク情報
DOI
https://doi.org/10.1016/S0167-2789(98)00313-3
ID情報
  • DOI : 10.1016/S0167-2789(98)00313-3
  • ISSN : 0167-2789
  • SCOPUS ID : 0040559986

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