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.
