Geometry of webs, Hamiltonian systems and complex dynamics

网络几何、哈密顿系统和复杂动力学

• 批准号: 10440014
• 负责人: NAKAI Isao
• 金额: $ 8.26万
• 依托单位: Ochanomizu University (1999-2000)Hokkaido University (1998)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440014/
• 关键词: WEB; Foliation; Complex dynamics; Quasi group; Caustics; Chern connection; difraction; co-tidal; Quasi Group; Chern 接続; 接触構造; 常微分方程式; 複素力学系; 正則ベクトル場; 可換力学系; Qunsi Group; 面積程存; 可換力学; CHERN接続

We defined a canonical affine connection for integrable first order partial differential equations of finite type, and investigated its singularities along the locus where the foliation structure of solutions degenerates. We proved there exists one to one correspondence of the moduli space of equations and the space of curvature forms in some cases. We proved also the triangulability of the mapping cylinder of generic smooth mappings of manifolds. As an application we proved a naturality formula of the stiefel-homology functor of constructible functions on manifolds to homology classes.

定义了可积一阶有限型偏微分方程的典范仿射联络，并研究了它沿解的叶状结构退化轨迹的沿着奇性。证明了在某些情况下，方程的模空间与曲率形式空间存在一一对应。证明了流形上一般光滑映射的映射柱的可三角化性。作为应用，我们证明了流形上可构造函数的stiefel-同调函子到同调类的一个自然公式。

项目成果

H.Sato: "Linearizations of ordinary differential equatione by area preserving maps" Nagoya Math.J.(in press). 153. (1999)

H.Sato：“通过面积保留映射对常微分方程进行线性化”Nagoya Math.J.（正在出版）。

T.Suwa: "Nash residne and Singular holomorphic foliations"Asian J.Math. (in press).

T.Suwa：“纳什残差和奇异全纯叶”亚洲 J.Math。

I,Nakai: "Web geometry and the eqvivalence problem of first order differential equations"Web geometry and related topics, World Scientific. (in press). (2000)

I，Nakai：“网络几何和一阶微分方程的等价问题”网络几何及相关主题，世界科学。

吉川 通彦: "Geometry of homogeneous left Lie loops and tangent Lie triple algebras"Mem. Fac. Sci. Eng. Shimane Univ.. B32. 57-68 (1999)

吉川道彦：“齐次左李环和正切李三重代数的几何”Mem Shimane Univ.. B32。

I.Nakai: "Web geometry and the equivalence problem of first order differential equations"Web geometry and related topics, world Scientific. (in press).

I.Nakai：“网络几何和一阶微分方程的等价问题”网络几何及相关主题，世界科学。