Analysis of non-hyperbolic systems through unstable periodic orbits

通过不稳定周期轨道分析非双曲系统

• 批准号: 23740065
• 负责人: SAIKI Yoshitaka
• 金额: $ 2.75万
• 依托单位: Hitotsubashi University (2013)Hokkaido University (2011-2012)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740065/
• 关键词: 力学系; カオス; 不安定周期軌道; リアプノフベクトル; リアプノフ解析; 多様体; 周期軌道; 数値計算; 非双曲系

Dynamical systems can be classified into two types hyperbolic systems and non-hyperbolic systems. Hyperbolic systems have been understood well since the Smale's work. In this study we focus on non-hyperbolic systems and obtained some results in (1) strongly non-hyperbolic case, and (2) the occurrence of non-hyperbolicity by using unstable periodic orbits. Based on these results we have constructed cycle expansion theory which works well for the Henon map of a non-hyperbolic parameter.

动力系统可分为双曲型系统和非双曲型系统。自斯梅尔的工作以来，双曲系统已经得到了很好的理解。本文主要研究了非双曲系统，并在(1)强非双曲情况下和(2)利用不稳定周期轨道出现非双曲情况下得到了一些结果。在此基础上，构造了适用于非双曲参数Henon映射的循环展开理论。

项目成果

Recognition of transition patterns in a business cycle model by unstable periodic orbits

通过不稳定周期轨道识别经济周期模型中的过渡模式

• 发表时间: 2011
• 期刊: International Journal of Bifurcation and Chaos
• 影响因子: 2.2
• 作者: Yata;K.;H. Hirai;Y. Saiki and M. Yamada;青嶋誠,矢田和善;H. Hirai;Yoshitaka Saiki and Michio Yamada;青嶋誠,矢田和善;H. Hirai;Y. Saiki and K. Ishiyama
• 通讯作者: Y. Saiki and K. Ishiyama

Time Averaged Properties Along Unstable Periodic Orbits of the Kuramoto-Sivashinsky Equation, Nankai Series in Pure

纯Kuramoto-Sivashinsky方程南开级数沿不稳定周期轨道的时间平均特性

• 发表时间: 2013
• 期刊: Applied Mathematics and Theoretical Physics, World Scientific
• 作者: Yata;K.;H. Hirai;Y. Saiki and M. Yamada
• 通讯作者: Y. Saiki and M. Yamada

Manifold structures of Unstable Periodic Orbits and the Appearance of a Periodic Window in Chaotic Systems

混沌系统中不稳定周期轨道的流形结构和周期窗的出现

• 发表时间: 2014
• 期刊: Physical Review E
• 影响因子: 2.4
• 作者: Inatsu;M.;N. Nakano;S. Kusuoka;and H. Mukougawa;M. U. Kobayashi and Y. Saiki
• 通讯作者: M. U. Kobayashi and Y. Saiki

非双曲力学系の不安定周期軌道解析

非双曲动力系统的不稳定周期轨道分析

• 发表时间: 2014
• 作者: 小谷野仁;林田守広;阿久津達也;齊木吉隆;齊木吉隆
• 通讯作者: 齊木吉隆

Economic intermittency in a two-country model of business cycles coupled by investment

投资耦合两国经济周期模型中的经济间歇性

• 发表时间: 2011
• 期刊: Chaos, Solitons and Fractals
• 作者: Y. Saiki;A. Chian and H. Yoshida
• 通讯作者: A. Chian and H. Yoshida