Mathematical Sciences: Approximating the Fractal Properties of Invariant Sets

该项目位于一般地区的离散和 连续动力系统和相关的不变集。 具体而言，目标是为 计算的误差和收敛性分析 不变集的维数 这些集合通常是分形的， 必须使用尺寸的性质和更一般的定义。 动力学通常与马尔可夫划分相关联 并且这些集合将支持伯努利概率度量。 该项目的另一个方面将是研究 动力系统中的混沌和不稳定性。 上述理论研究与 各种生物、化学和物理系统的行为 涉及动力学。

This project lies in the general area of discrete and continuous dynamical systems and the associated invariant sets. In particular, the goal is to develop a framework for the analysis of error and convergence for the calculation of the dimension of invariant sets. These sets are often fractal in nature and more general definitions of dimension must be used. The dynamics will usually be associated with a Markov partition and the sets will support a Bernoulli probability measure. Another aspect of the project will be a study into the onset of chaos and intermittency in dynamical systems. The theoretical study described above has relevance to the behavior of various biological, chemical and physical systems involving dynamics.