Symmetry and the Singular Point Analysis for Ordinary Differential Equations : General and Mathematical Physics
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概要
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We show a direct relation between the singular point analysis and the symmetry for ordinary differential equations. It is proved that a system with a meromorphic solution allows Laurent solutions depending on m arbitrary parameters if it has m independent symmetries, regardless of the existence of single-valued first integrals. Applying the result to Hamiltonian systems, we show a pairing property and introduce a new definition of integrability as a synthesis of symmetries and first integrals. Further we deal with integrable Hamiltonian systems whose first integrals are in involution and discuss a relation between their symmetries and infinitely multi-valued first integrals yielded by Liouville's quadrature.
- 理論物理学刊行会の論文
- 1992-05-25
著者
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ISHII Masaharu
Department of Biotechnology, The University of Tokyo
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Ishii Masaharu
Department Of Biotechnology Graduate School Of Agricultural And Life Sciences The University Of Toky
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ISHII Masaharu
Department of Physics, Nagoya University
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ISHII Masaharu
Department of Agricultural Chemistry, The University of Tokyo
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