MIXING STUDIES USING HORSESHOES

The ability to recognize and classify horseshoe generated structures is important in mixing problems. In this paper, we develop techniques to study higher iterations of horseshoe maps, by exploiting a method for representing them in a convenient mathematical notation. We show how to keep track of mixing of various blob segments over a number of iterations. Multiple iterations are investigated and an algorithm is developed in order to compute the higher iterations of the original horseshoe. Using similar ideas we present a method to keep track of thicknesses of the various blob striations. In a chaotic flow, complicated patterns can develop due to rapid stretching and folding. The tools developed in this paper would help determine the underlying cause of these patterns, i.e., identify the generating horseshoe.