Formal Paths, Iterated Integrals and the Center Problem for Ordinary Differential Equations

迭代测试驱动开发的形式化分析

A Formal Analysis of Iterated TDD

本文形式化分析迭代测试驱动开发，定义关键概念，证明在特定上下文中可稳定生成正确代码，否则呈混沌行为，并解释早期研究结果差异。

傅里叶变换与迭代函数系统

Fourier transforms and iterated function systems

本文探讨迭代函数系统平稳测度傅里叶变换的界定问题，综述了源于算术、代数及几何伪随机性的影响，并概述了热力学形式、加性组合、随机游走及双曲动力学等方法，同时提及开放问题与量子混沌关联。

D-凹非自治标量常微分方程中吸引子与极小集的分岔理论

Bifurcation Theory of Attractors and Minimal Sets in D-Concave Nonautonomous Scalar Ordinary Differential Equations

本文利用斜积框架研究D-凹非自治标量常微分方程的单参数分岔，刻画极小集数量与性质及全局吸引子形状的突变机制。

收敛到正规矩阵的一族矩阵流

A family of matrix flows converging to normal matrices

本文提出了一族收敛到正规矩阵的矩阵流，通过常微分方程定义，并探讨了其在不同数学结构中的应用。

Normal Forms of second order Ordinary Differential Equations $y_{xx}=J(x,y,y_{x})$ under Fibre-Preserving Maps

We study the equivalence problem of classifying second order ordinary differential equations $y_{xx}=J(x,y,y_{x})$ modulo fibre-preserving point transformations $x\longmapsto φ(x)$, $y\longmapsto ψ(x,y)$ by using Moser's method of normal forms. We first compute a basis of the Lie algebra ${\frak{g}}_{{\{y_{xx}=0\}}}$ of fibre-preserving symmetries of $y_{xx}=0$. In the formal theory of Moser's method, this Lie algebra is used to give an explicit description of the set of normal forms $\mathcal{N}$, and we show that the set is an ideal in the space of formal power series. We then show the exist…