Proceeding of International Conference
Tetsushi Ueta, Kei Nagao, Accurate Formulas Locating Unstable Periodic Points in Chaos, Proc. NOLTA2010, 111-114, Cracow, Sep. 2010.
Abstract: We have studied fractal nature of patterns given by the directional coloring for chaotic attractors. With this method, unstable periodic points are visualized as concentrated points or crossing points in the state space. A fractal pattern around the specific unstable fixed point are identified as a formula derived from relationship among neighbor unstable periodic points. In this paper, we try to model an accurate formula giving locations of unstable periodic points. Higher periodic points are predicted by the obtained formula. Some numerical examples are shown.