Creation of coherent structures in area-preserving maps

Abstract

We propose a new method for the creation of coherent structures in two-dimensional area-preserving maps. The coherent structures are created by applying a parameter perturbation in the neighbourhood of the periodic points of the map. We demonstrate the success of our method in the case of the standard map and in two cases of maps which represent realistic fluid flows, the blinking vortex map of Aref and the journal bearing map of Chaiken. We also find the signatures of the coherent structures in quantifiers like the local exit time distribution and of the local Lyapunov exponents of the system. Our method may provide useful insights into the ways in which coherent structures are created in natural systems.