Mathematical Sciences: Pressure and Local Entropy in Dynamical Systems

数学科学：动力系统中的压力和局部熵

• 批准号: 9106307
• 负责人: Nicolai Haydn
• 金额: $ 5.12万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106307&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Pressure; Local; Entropy

Professor Haydn will study dynamical systems using a local entropy function. There are three areas where this concept will be applied. First, Professor Haydn will use it to find a formula which determines the Hausdorff dimension of a hyperbolic set. Second, he will use it to find the singularity spectrum of for higher dimensional dynamical systems. Finally, a somewhat finer tool will be used to investigate escape rates for non-attractors. A dynamical system can be thought of as a system which evolves in time with a definite well defined law. For example, given the initial state of a fluid, at least theoretically one can use the Navier-Stokes equations to predict the state of the fluid at any later time. However, this evolution is so complicated, even chaotic, that one must look for general ways of describing the evolution without actually solving the equations. This is the realm of the field of dynamical systems and the driving force behind the research of Professor Haydn.

海顿教授将使用局部熵功能研究动力系统。 在三个领域，将应用此概念。 首先，海顿教授将使用它来找到一个确定双曲线套件的Hausdorff尺寸的公式。 其次，他将使用它来找到更高维动力系统的奇异性频谱。 最后，将使用一个更好的工具来研究非吸引者的逃生率。 可以将动态系统视为随着确定的明确定义法律而演变的系统。 例如，给定流体的初始状态，至少从理论上讲，人们可以在任何以后的时间使用Navier-Stokes方程来预测流体状态。 但是，这种进化是如此复杂，甚至混乱，以至于必须寻找描述进化的一般方法，而无需实际求解方程。 这是Haydn教授研究背后动态系统领域的领域。