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<p>The initial value spaces of the Painlevé equations are proposed by Okamoto. They are symplectic manifolds in which the Painlevé equations are described as polynomial Hamiltonian systems on all coordinates. In this article, we construct an initial value space of the four dimensional Painlevé system with affine Weyl group symmetry of type <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((A_5+A_1)^{(1)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mn>5</mn> </msub> <mo>+</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>.</p>

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Initial Value Space of the Four Dimensional Painlevé System with \((A_5+A_1)^{(1)}\) Symmetry

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月23日

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  • Kazuya Matsugashita,
  • Takao Suzuki

摘要

The initial value spaces of the Painlevé equations are proposed by Okamoto. They are symplectic manifolds in which the Painlevé equations are described as polynomial Hamiltonian systems on all coordinates. In this article, we construct an initial value space of the four dimensional Painlevé system with affine Weyl group symmetry of type \((A_5+A_1)^{(1)}\) ( A 5 + A 1 ) ( 1 ) .