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In recent years scientific visualization has been driven by the need to visualize high-dimensional data sets within high-dimensional spaces. However most visualization methods are designed to show only some statistical features of the data set. The paper deals with the visualization of trajectories of high-dimensional dynamical systems which form a L n n data set of a smooth n-dimensional flow. Three methods that are based on the idea of parallel coordinates are presented and discussed. Visualizations done with these new methods are shown and an interactive visualization tool for the exploration of high-dimensional dynamical systems is proposed.