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2変数退化ガルニエ系の代数解と,代数解による代数構造の解析
http://hdl.handle.net/10076/13758
http://hdl.handle.net/10076/13758e751438d-4dac-4b45-a2d6-5a09890b35aa
名前 / ファイル | ライセンス | アクション |
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20K16702.pdf (279.3 kB)
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Item type | 報告書 / Research Paper(1) | |||||
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公開日 | 2014-03-10 | |||||
タイトル | ||||||
言語 | ja | |||||
タイトル | 2変数退化ガルニエ系の代数解と,代数解による代数構造の解析 | |||||
言語 | ||||||
言語 | jpn | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | ガルニエ系 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 有理解 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 代数解 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 差分パンルヴェ方程式 | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_18ws | |||||
資源タイプ | research report | |||||
著者 |
川向, 洋之
× 川向, 洋之 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | (1)木村氏の定義した退化ガルニエ系G(3,1,1)と,研究代表者の定義した退化ガルニエ系G(5/2,1,1)を考察し,G(3,1,1)とG(5/2,1,1)の有理解をすべて決定した.(2)木村氏の定義した退化ガルニエ系G(3,2)の代数解をすべて決定した.(3)(1),(2)の結果を用いて,退化ガルニエ系G(5/2,1,1),G(3,1,1),G(3,2)が双有理な変換で写りあわないことを示した.(4)リーマン球面上で3つの確定特異点を持つ3階のフックス型方程式を考察し,このシュレジンガー変換が差分のVI型パンルヴェ方程式になることを示した.また同様の考察を行えば差分ガルニエ系を構成できることを示した. | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | (1) We consider degenerate Garnier systems G(3,1,1) (which is defined by H.Kimura) and G(5/2,1,1) (which is defined by H.Kawamuko), and find all rational solutions of each equation.(2) We consider degenerate Garnier system G(3,2) (which is defined by H.Kimura), and find all algebraic solutions of G (3,2).(3) By using the results (1) and (2), we show that there is no birational transformation between these systems.(4) We consider a third order Fuchsian differential equation which has three regular singular points on Riemann sphere, and show that the Schlesinger transformation is equivalent to a difference VI Painlev\'e equation. Moreover, we can define a difference Garnier system in a similar way. | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 平成20~22年度科学研究費補助金(基盤研究(C))研究成果報告書 | |||||
書誌情報 |
発行日 2011-04-25 |
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フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
その他のタイトル | ||||||
Analysis of an algebraic structure of a degenerate Garnier system from a viewpoint of algebraic solutions | ||||||
出版者 | ||||||
出版者 | 三重大学 | |||||
科研費番号 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 20540207 | |||||
資源タイプ(三重大) | ||||||
Kaken / 科研費報告書 |