Different Methods of Partitioning the Phase Space of a Dynamic System

Abstract

In symbolic dynamics, the definition of a symbolic sequence from a continuous times series depends on the use of an appropriate par-tition of the phase space. In fact, the best way is to estimate a gen-erating partition. However, it is not possible to find generating partitions for most ex-perimental observations because such partitions do not exist when noise is present. In this paper, different partition methods applied to stochastic and chaotic system will be compared in order to choose one which con-serves system entropy rate. This partition is called a Markov parti-tion.