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The first Painleve equation is expressed as a vector field on the three dimensional weighted projective space CP^3(3,2,4,5). With the aid of the dynamical systems theory and the orbifold structure of ...CP^3(3,2,4,5), a simple proof of the Painleve property and the construction of the space of initial conditions are given.In particular, Painleve's transformation is geometrically derived, which proves to be a Darboux coordinates of a certain algebraic surface with a holomorphic symplectic form.続きを見る
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Mendeley出力
