Mathematical Sciences: Pressure and Local Entropy in Dynamical Systems

海顿教授将研究动力系统使用本地 熵函数 这一概念将在三个方面得到体现， 应用。 首先，海顿教授会用它找到一个公式 它决定了双曲集的Hausdorff维数 第二，他将用它来寻找的奇异谱， 高维动力系统 最后，一个更好的 工具将用于调查非吸引子的逃逸率。 一个动力系统可以被认为是一个进化的系统， 在一个明确的时间定义的法律。 例如，给定 流体的初始状态，至少理论上可以使用 Navier-Stokes方程预测流体的状态在任何 晚些时候。 然而，这种演变是如此复杂，甚至 混沌，人们必须寻找描述 而不需要解方程。 这是 动力系统领域及其驱动力 海顿教授的研究背后

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.