Fractal basin boundaries

Steven W. McDonald, Celso Grebogi, Edward Ott, James A. Yorke

Research output: Contribution to journalArticlepeer-review

557 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)125-153
Number of pages29
JournalPhysica. D, Nonlinear Phenomena
Issue number2
Publication statusPublished - Oct 1985


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