Theoretical Study of Chaotiic Phenomena of Non-invertible Sysytems

不可逆系统混沌现象的理论研究

• 批准号: 08454045
• 负责人: AOKI Nobuo
• 金额: $ 3.07万
• 依托单位: TOKYO METROPOLITAN UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08454045/
• 关键词: non-equilibrium; media; Ginzbrug-Landau equation; stability; Axiom A; strong transversality; inverse; キンズブルクグ-ランダウ方程式; 非双曲型; 双曲型測度; SBR測度

Recently many chain and lattice models of non-equilibrium media have been of great interest. It is known that some types of motions of non-equilibrium media can be described by a space and time-discreate version of the Ginzburg-Landau equation. In the case of one-component and one-dimensional media this leads to the equationu_j(n+1)=f(u_j(n))*g({u_i(n)}^<j+g>_-g)n, j*Z,where f nd g are C^2-maps and u_j(n)*R^d.In order to study stability of motions in lattice models of this type, we gave an answer for the following question which was remained as a major open problem : "Axiom A endomorphisms with strong transversarity are inverse limit stable"

近年来，非平衡介质的链格模型引起了人们极大的兴趣。众所周知，非平衡介质的某些类型的运动可以用Ginzburg-Landau方程的时空离散形式来描述。在单组分一维介质的情况下，这导致方程u_j（n+1）=f（u_j（n））*g（{u_i（n）}^<j+g>_-g）n，j*Z，其中f和g是C^2-映射，u_j（n）*R^d。为了研究这种类型的格点模型中运动的稳定性，我们给出了以下问题的答案，该问题仍然是一个主要的开放问题：“公理A具有强横截性的自同态是逆极限稳定的”

项目成果

N.AOKI: "Differentiable maps havimg hyperbolic sets" Topology and its Applications. (in press).

N.AOKI：“具有双曲集的可微映射”拓扑及其应用。

青木統夫: "共立出版" 力学系・カオス, 413 (1996)

Motoo Aoki：“Kyoritsu Shuppan”动力系统/混沌，413 (1996)

S.Yamashita: "The Do in care density of a domain on the Riemainian sphere" Math.Japonica. 41. 621-624 (1995)

S.Yamashita：“黎曼球面上域的关心密度”Math.Japonica。

H.Takai, T.Sudo: "Stable rank of the C^<**>-algebras of nilpotent Lie group" International J.Math.Vol.6. 439-446 (1995)

H.Takai、T.Sudo：“幂零李群的 C^<**>-代数的稳定秩”International J.Math.Vol.6。

S.Yamashita: "The poincare density of a domain on the Riemannian spheil" Math.Japanica. 41. 621-624 (1995)

S.Yamashita：“黎曼球上域的庞加莱密度”Math.Japanica。