Phase space partition with Koopman analysis.

Abstract

Symbolic dynamics is a powerful tool to describe topological features of a nonlinear system, where the required partition, however, remains a challenge for some time due to the complications involved in determining the partition boundaries. In this article, we show that it is possible to carry out interesting symbolic partitions for chaotic maps based on properly constructed eigenfunctions of the finite-dimensional approximation of the Koopman operator. The partition boundaries overlap with the extrema of these eigenfunctions, the accuracy of which is improved by including more basis functions in the numerical computation. The validity of this scheme is demonstrated in well-known 1D and 2D maps.