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math.CA2019
Uniqueness of polarization for the autonomous 4-dimensional Painlevé-type systems
Akane Nakamura, Eric Rains
We prove that for any autonomous 4-dimensional integral system of Painlevé type, the Jacobian of the generic spectral curve has a unique polarization, and thus by Torelli's theorem…
math.CA2015★ 6 cited
Autonomous limit of 4-dimensional Painlevé-type equations and degeneration of curves of genus two
Akane Nakamura
Higher dimensional analogs of the Painlevé equations have been proposed from various aspects. In recent studies, 4-dimensional analogs of the Painlevé equations were classified int…
math.CA2012★ 28 cited
Degeneration scheme of 4-dimensional Painlevé-type equations
Hiroshi Kawakami, Akane Nakamura, Hidetaka Sakai
Four 4-dimensional Painlevé-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, th…