Symmetry Groups of AnA_n Hypergeometric Series

Structures of symmetries of transformations for Holman-Biedenharn-Louck $A_n$ hypergeometric series: $A_n$ terminating balanced ${}_4 F_3$ series and $A_n$ elliptic ${}_{10} E_9$ series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each types of $A_n$ hypergeometric series are given. Among them, a "periodic" affine Coxeter group which seems to be new in the literature arises as an invariance group for a class of $A_n$ ${}_4 F_3$ series

Variational Structures for Infinite Transition Orbits of Monotone Twist Maps

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of area-preserving maps, we define a special class of area-preserving maps called monotone twist maps. Variational structures determined from twist maps can be used for constructing characteristic trajectories of twist maps. Our goal is to prove the existence of an infinite transition orbit, which represents an oscillating orbit between fixed points infinite times, through minimizing methods.Comment: arXiv admin note: substantial text overlap with arXiv:2212.0185

ツイスト写像とn体問題に関する最小化法及び関連する話題

京都大学新制・課程博士博士(情報学)甲第24328号情博第812号新制||情||137(附属図書館)京都大学大学院情報学研究科数理工学専攻(主査)准教授 柴山 允瑠, 教授 矢ヶ崎 一幸, 教授 山下 信雄, 教授 田口 智清学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA