論文 - 中村 あかね
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Discrete Hamiltonians of discrete Painlevé equations 査読あり
Takafumi Mase, Akane Nakamura, Hidetaka Sakai
Annales de la Faculté des sciences de Toulouse : Mathématiques 6 ( 29 ) 1251 - 1264 2021年04月
記述言語：英語 掲載種別：研究論文（学術雑誌）
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Uniqueness of polarization for the autonomous 4-dimensional Painlevé-type systems 査読あり 国際誌
Akane Nakamura, Eric Rains
International Mathematics Research Notices 2020年02月
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The Painlevé divisors of the autonomous 4-dimensional Painlevé-type equations 査読あり
Akane Nakamura
2020年
記述言語：英語 掲載種別：研究論文（学術雑誌）
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Autonomous limit of 4-dimensional Painlevé-type equations and degeneration of curves of genus two 査読あり 国際誌
Annales de l'Institut Fourier 69 ( 2 ) 845 - 893 2019年
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Degeneration scheme of 4-dimensional Painlevé-type equations 査読あり
H. Kawakami, H. Sakai
MSJ Memoir 37 25 - 111 2018年
記述言語：英語 掲載種別：研究論文（学術雑誌）
Four 4-dimensional Painlev\'e-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, the Sasano system, and the sixth matrix Painlev\'e system. Degenerating these four source equations, we systematically obtained other 4-dimensional Painlev\'e-type equations. If we only consider Painlev\'e-type equations whose associated linear equations are of unramified type, there are 22 types of 4-dimensional Painlev\'e-type equations: 9 of them are partial differential equations, 13 of them are ordinary differential equations. Some well-known equations such as Noumi-Yamada systems are included in this list. They are written as Hamiltonian systems, and their Hamiltonians are neatly written using Hamiltonians of the classical Painlev\'e equations.
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Two aspects of the theta divisor associated with the autonomous Garnier system of type 9/2 査読あり
Akane Nakamura
JMM 10, Representation Theory and Differential Equations 2017年
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（大学，研究機関等紀要）
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Autonomous limit of 4-dimensional Painlevé-type equations and degeneration of curves of genus two
Akane Nakamura
2015年03月
記述言語：英語 掲載種別：学位論文（その他）
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Toward a classification of four-dimensional Painlevé-type equations 査読あり
Hiroshi Kawakami, Akane Nakamura, Hidetaka Sakai
AMS Contemporary mathematics 593 2013年
記述言語：英語 掲載種別：研究論文（学術雑誌）