Ergodic Theory and Visualization I: Visualization of Ergodic Partition and Invariant Sets

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Abstract
We present a computational study of the invariant sets visualization method based on ergodic partition theory, firstly proposed in [1]. The algorithms for computation of the time averages of many L1 functions are developed and employed producing the approximation of the phase space ergodic partitioning. The method is exposed in the context of discrete-time dynamical systems producing a graphical representation of the phase space in terms of the invariant set structure that gives a substantial insight into the global and local properties of the dynamics. We used the Chirikov standard map in order to show the implementation of the method, followed by applications to other multi-dimensional maps. We extend the study in the paper to follow [2] by examining the visualization of periodic sets using harmonic time averages constructed in [3].

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