Mathematical Sciences: Approximating the Fractal Properties of Invariant Sets

本课题属于离散和连续动力系统及其相关的不变量集的一般领域。特别是，目标是开发一个框架的误差分析和收敛的计算不变集的维数。这些集合在本质上通常是分形的，必须使用更一般的维数定义。动力学通常与马尔可夫划分相关联，集合将支持伯努利概率度量。该项目的另一个方面将是对动力系统中混沌和间歇性的开始进行研究。上述理论研究与涉及动力学的各种生物、化学和物理系统的行为有关。

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.