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Fractal basin boundaries |
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| Authors: | Steven W McDonald Celso Grebogi Edward Ott James A Yorke |
| Institution: | 1. Laboratory for Plasma and Fusion Energy Studies, University of Maryland, College Park, MD 20742, USA;2. Department of Electrical Engineering and Department of Physics and Astronomy, University of Maryland, College Park, MD 20742, USA;3. Department of Mathematics and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742, USA |
| Abstract: | Basin boundaries for dynamical systems can be either smooth or fractal. This paper investigates fractal basin boundaries. One practical consequence of such boundaries is that they can lead to great difficulty in predicting to which attractor a system eventually goes. The structure of fractal basin boundaries can be classified as being either locally connected or locally disconnected. Examples and discussion of both types of structures are given, and it appears that fractal basin boundaries should be common in typical dynamical systems. Lyapunov numbers and the dimension for the measure generated by inverse orbits are also discussed. |
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