Research on ergodic theory and Perron-Frobenius operator

遍历理论与Perron-Frobenius算子研究

• 批准号: 12640190
• 负责人: MORI Makoto
• 金额: $ 1.66万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640190/
• 关键词: ergodic theory; Perron-Frobenius Operator; fractal; random number; Brownian motion; スペクトル; Perron-Frobenius作用素; エルゴード性; 混合性

We have constructed low discrepancy sequences using dynamical system. Our main tool is the spectra of the Perron-Frobenius operator associated with the dynamical system.We calculate the Hausdorff dimensions of the fractals generated by dynamical systems, and at the same time we study the ergodic properties of the dynamical system on fractals. We studied a phase transition of a one parameter family of fractals.Using random walks generated by dynamical systems, we construct a Brownian motion and calculate the order of convergence.

我们使用动力系统构建了低差异序列。我们的主要工具是与动力系统相关的Perron-Frobenius算子的谱。我们计算动力系统产生的分形的Hausdorff维数，同时研究动力系统在分形上的遍历性质。我们研究了分形的单参数族的相变。利用动力系统生成的随机游走，我们构造了布朗运动并计算了收敛阶。

项目成果

Makoto Mori: "Cantor sets generated by Piecewise linear map"The Inst.of Natural Sciences Nihon Univ.. 35. 1-27 (2001)

Makoto Mori：“由 Piecewise 线性映射生成的 Cantor 集”The Inst.of Natural Sciences Nihon Univ.. 35. 1-27 (2001)

K.Watanabe,K.Yoshida: "Hilbert-Kunz multiplicity of two dimensional local rings"Nagoya.Math.J.. (to appear).

K.Watanabe，K.Yoshida：“二维局部环的 Hilbert-Kunz 重数”Nagoya.Math.J..（待出现）。

Makoto Mori: "Pseudo random sequences generated by piecewise linear maps from the view point of dynamical system"Mathematics and Computers in Simulation. 55. 177-179 (2001)

Makoto Mori：“从动力系统的角度来看分段线性映射生成的伪随机序列”模拟中的数学和计算机。

Makoto Mori: "Higher Order mixing property of piecewise linear transformation"Discrete and Continous Dynamical systems. 6. 915-934 (2000)

Makoto Mori：“分段线性变换的高阶混合特性”离散和连续动力系统。

Osamu Suzuki: "The Riemann-Hilbert problems for higher dimensional homology groups on a real manifold"the proceeding of the International Conference on Boundary Value Problems. (to appear). (2000)

Osamu Suzuki：“实流形上高维同调群的黎曼-希尔伯特问题”国际边值问题会议论文集。