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Phys. Rev. Lett. 82, 3597–3600 (1999)

Sporadically Fractal Basin Boundaries of Chaotic Systems

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Brian R. Hunt* and Edward Ott†
University of Maryland, College Park, Maryland 20742

Epaminondas Rosa, Jr.
Nonlinear Dynamics Laboratory, Department of Physics, University of Miami, Coral Gables, Florida 33146

Received 17 November 1998; published in the issue dated 3 May 1999

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 dimensions 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.

© 1999 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.82.3597
DOI:
10.1103/PhysRevLett.82.3597
PACS:
05.45.Ac

*Department of Mathematics and Institute for Physical Sciences and Technology. Electronic address: bhunt@ipst.umd.edu

†Institute for Plasma Research, Institute for Systems Research, and Departments of Electrical Engineering and of Physics.

 
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