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年的项目：研究图3和4的多项式图的模量空间以及四二个理性图的研究。特别是我们分析了双曲线成分。 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）地图的模量空间，有两个关键点，第1期特刊，《科学典范》，乔萨尔大学的科学bulitin。 pp。99-113Project，1998年：多项式多项式模量的Alfine结构的研究，并表征了逃生基因座。 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具有第四学位的多项式，第4期专刊，Josai大学的科学牛。 pp。83-94（4）一维图的家族的俯仰叉分叉图，kyouto Univ。 Kokyu-Roku No.1031（5）多项式地图的分支基因座，Kyouto Univ。 Kokyu-Roku No。 1042（6）1-parmeter 1维家族，具有非符号分叉图，Kyouto Univ。 Kokyu-Roku No。 1049年国际大会和双曲线组件，NACA98，Niigata，7月28日至31日，1998年1998年沿代数曲线的偶然分叉，ICDEA98，波兰，8月25日至29日，1998年8月25日

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

NISHIZAWA,kiyoko: "Moduli spaces of Polynomial Maps with Degree Four" Josai Information Sciences Researches. 9. 1-10 (1998)

西泽清子：“四次多项式映射的模空间”城西信息科学研究。