Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems

Ramen Ghosh, Mahmoud Tahmasebi, Marion McAfee

Abstract: The article aims to demonstrate the effectiveness of using the Koopman operator and dynamic mode decomposition (DMD) for iterated function systems (IFS). Specifically, we show how these tools can be used to analyze and predict the behaviour of stochastic nonlinear dynamical systems represented by discrete-time Markov chains on a compact state space. In particular, we focus on an ergodic nonlinear IFS, which has not been studied with these approaches before. Our paper presents the first application of dynamic mode decomposition to this type of system.