Sporadically Fractal Basin Boundaries of Chaotic Systems

Brian R. Hunt, Edward Ott, and Epaminondas Rosa, Jr.

Phys. Rev. Lett. 82 (1999), 3597-3600.

Online abstract and download information

We demonstrate a new type of basin boundary for typical chaotic dynamical systems. For the case of a two dimensional map, this boundary has the character of the graph of a function that is smooth and differentiable except on a set of fractal dimension less than one. In spite of the basin boundary being smooth ``almost everywhere'', its fractal dimension exceeds one (implying degradation of one's ability to predict the attractor an orbit approaches in the presence of small initial condition uncertainty). We call such a boundary sporadically fractal.

• Figure 1a, PostScript (1400K)
• Figure 1b, PostScript (20K)
• Figure 1c, PostScript (200K)
• Figure 2, PostScript (20K)

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