Estimating generating partitions of chaotic systems by unstable periodic orbits

An outstanding problem in chaotic dynamics is to specify generating partiti ons for symbolic dynamics in dimensions larger than 1. It has been known th at the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions de fined with respect to periodic orbits. Our algorithm allows us to obtain th e approximate location of the generating partition for the Ikeda-Hammel-Jon es-Moloney map.