Proceeding of International Conference
Tetsushi Ueta, Hiroshi Kawakami, Visualization of unstable periodic points embedded in chaotic attractors by the directional coloring, Proc. NOMA'07, 25-28, Toulouse, Dec. 2007.
Abstract: We propose a new visualization method called directional coloring for chaotic attractors in two-dimensional discrete systems. The argument defined by the current point of the solution orbit and its n-th mapped point is assigned into the hue circle in the HSV color system. For a given system, the vector field of the n-th powered system is visualized by this method. As singular points, n-periodic points are emerged as concentrating points of colors. We also reduce the computation time by featuring the brute-force method for the directional coloring, and illustrate a detection method of unstable periodic points in a chaotic attractor as an application.