Computation and Visualization of Invariant Sets of Dynamical Systems

Igor Mezic and Linda Petzold

Computation and Visualization of Invariant Sets of Dynamical Systems is a very important tool in the analysis of chaotic systems. It gives valuable information about the global dynamics and qualitative behaviour of the system without having to solve the underlying dynamical system explicitly. Here, we attack the problem from the point of view of the so-called Koopman operator and apply it on the Standard Map. The above figure shows the dynamics of the computed invariant sets of the Standard Map with respect to a parameter.