Study of Complex Dynamical Systems of rational functions

有理函数复杂动力系统研究

• 批准号: 09640217
• 负责人: NISHIZAWA Kiyoko
• 金额: $ 1.09万
• 依托单位: Josai University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640217/
• 关键词: complex Dynamical Systems; Moduli Space; algebraic manifold; hyperbolic component; affine structure; chaos; bifurcation diagram.; topological entropy.; アフィン構造; 自己同型群; カオス分岐現象; フラクタル

Project of 1997 : Study of Moduli spaces for the polynomial maps with degree 3 and 4 and for the quadartic rational maps. Especially we analyzed hyperbolic components. And we construct a counter example to the Nusse-Youke's conjecture of monotonoe bifurcation diagrams.(1) Non-monotone bifurcations for Quadratic rational functions {mf(x)}m, Nonlinear Analysis , 30, pp.1497 -1504(2) Moduli spaces and and symmetry loci of polynomial maps, Proceedings of ISSAC'97, pp.342 - 342(3) Moduli spaces of maps with two critical points, special issue no.1, Science Bulitin of Josal Univ. pp. 99 - 113Project of 1998 : Study of alfine structure of the moduli sapce of the polynomials with degree 4, and characterize the escape locus. And we give two examples to the monotonicity and antinonotoniciyt conjectures.(1) Chaotic bifurcation of one parameter family, Josai Nonlinear Analysis, 30, pp.1497 - 1504(2) Moduli spaces and and symmetry loci of polynomial maps, Proceedings of ISSAC'97, pp.342 - 342(3) Two affine structures imposed in the polynomials with degree four, Special issue no.4, Science Bulltin of Josai Univ. pp. 83 - 94(4) Bothways pitch-fork bifurcation diagrams of family of one dimensional maps, Kyouto Univ. Kokyu-roku no.1031(5) Branch locus of polynomial maps, Kyouto Univ. Kokyu-roku no. 1042(6) 1-parmeter 1-dimensional family with non-monotone bifurcation diagram, Kyouto Univ. Kokyu-roku no. 1049International CongressBifurcations and hyperbolic components, NACA98, Niigata July 28 - 31 1998Chaotic bifurcations along algebraic curves, ICDEA98, Poland Aug 25 - 29 1998

1997年项目：研究3次和4次多项式映射和二次有理映射的模空间。特别是我们分析了双曲分量。并构造了单调分歧图的Nusse-Youke猜想的一个反例。(1)二次有理函数{mf（x）}m的非单调分支，非线性分析，30，pp.1497 - 1504（2）多项式映射的模空间和对称轨迹，ISSAC'97会议录，pp.342 - 342（3）具有两个临界点的映射的模空间，特刊no.1，Josal大学科学出版社，pp. 99 - 1131998年课题：研究四次多项式模空间的精细结构，并刻画其逃逸轨迹。并给出了单调性和反单调性的两个例子。(1)（2）多项式映射的模空间和对称轨迹，ISSAC'97会议录，pp.342 - 342（3）四次多项式中的两个仿射结构，Special issue no.4，Science Bulltin of Josai Univ. 83 - 94（4）一维映射族的双向分叉图，Kyoto Univ. Kokyu-roku no.1031（5）多项式映射的分支轨迹，Kyoto Univ. Kokyu-roku no.1042（6）具有非单调分叉图的1-parmeter一维映射族，Kyoto Univ. Kokyu-roku no.1049国际会议分叉和双曲分量，NACA 98，新泻July 28 - 31 1998 Chaotic bifurcations沿着algebraic curves，ICDEA 98，波兰Aug 25 - 29 1998

项目成果

Andrew Ranicki, Masayuki Yamasaki: "Controlled K-theory" Topolo.and its Appl.61-1. 1-59 (1995)

Andrew Ranicki、Masayuki Yamasaki：“受控 K 理论”Topolo. 及其 Appl.61-1。

Kiyoko Nishizawa, Masayo Fujimura: "Moduli spaces and symmetry loci of polynimial maps" Proc.of ISSA '97, ACM. 342-348 (1997)

Kiyoko Nishizawa、Masayo Fujimura：“多项式映射的模空间和对称轨迹”Proc.of ISSA 97，ACM。

山口 博: "On the product of Riesg Sets in dual objects of conpact groups" Hokkaido Univ.Technical. Rep, Series.in Math.57. 89-91 (1999)

Hiroshi Yamaguchi：“关于紧群对偶中的 Riesg 集的乘积”北海道大学代表，Math.57（1999）。

NISHIZAWA,kiyoko: "Non-Montome Bifurcations for Onadratic Rational Function {mf(x)}m" Nonlinear Analysis,Theory,Methods & Applications. 30. 1497-1504 (1997)

西泽清子：“Onadratic 有理函数 {mf(x)}m 的非 Montome 分岔”非线性分析、理论、方法

Kiyoko Nishizawa, Masayo Fujimura: "Moduli spaces of maps with two critical pionts" SBJU. Special Issue 1. 99-114 (1997)

Kiyoko Nishizawa、Masayo Fujimura：“具有两个关键点的地图的模空间”SBJU。