Mathematical Sciences: A Research Initiation for Undergraduates Students: Difference Equations and Chaos

一个支持六名学生的REU网站项目将获得 通过这个奖项。 针对问题的研究 产生于差分方程领域，重点是 理解溶液的混沌行为。 差分方程在数学中很自然地出现 从多个来源分析。 其中最重要的发生在 微分方程的离散近似，其中 衍生物被差异所取代。 振动理论 这些方程只需要很少的数学背景 一阶差分的动力学性质研究 方程组可以简化为连续迭代的研究 在有限区间上的函数 这个项目将强调两个观点。 第一 涉及高阶差分的定性性质 方程，尤其是三阶和四阶方程。的 该项目的第二个重点将是研究一阶 差分方程作为简单动力系统的例子， 其中特定的轨道结构和分叉性质 方程组将被采用。 的重要性 差分方程在机械振动的研究中， 数学生物学和经济学将受到重视。

An REU site project supporting six students will receive funding through this award. Research directed toward problems arising in the field of difference equations with a focus on understanding chaotic behavior of solutions will be carried out. Difference equations occur naturally in mathematical analysis from many sources. One of the most important occurs in discrete approximations to differential equations in which derivatives are replaced by differences. The oscillation theory of these equations requires very little mathematical background and the study of dynamical properties of first order difference equations can be reduced to the study of iterations of continuous functions over finite intervals. This project will emphasize two points of view. The first concerns qualitative properties of higher order difference equations, especially those of third and fourth order. The second thrust of the project will be the study of first order difference equations as examples of simple dynamical systems, where the orbit structure and bifurcation properties of specific families of equations will be taken up. The importance of difference equations in the study of mechanical vibrations, mathematical biology and economics will be emphasized.