Wada Basin Boundaries in Chaotic Scattering

Int. J. Bifurcation and Chaos 6, 251-266 (1996).
Leon Poon^1,2, José Campos³, Edward Ott^1,2,4, and Celso Grebogi^1,5
University of Maryland, College Park, MD 20742

Abstract

Chaotic scattering systems with multiple exit modes typically have fractal phase space boundaries separating the sets of initial conditions (basins) going to the various exits. If the exits number more than two, we show that the system may possess the stronger property that any initial condition which is on the boundary of one exit basin is also simultaneously on the boundary of all the other exit basins. This interesting property is known as the Wada property and basin boundaries having this property are called Wada basin boundaries.

1. Institute for Plasma Research
2. Department of Physics
3. Permanent Address: Universidad Interamericana de Puerto Rico, Recinto de Bayamón, Urb. Industrial Minillas, Bayamón, PR 00959
4. Department of Electrical Engineering and Institute for System Research
5. Department of Mathematics and Institute for Physical Sciences and Technology

Table of Contents

• Introduction
• Background
• Basin Boundary Structure of the Three-disk Model
• Verification of Wada Basin Boundaries
• Accessible and Inaccessible Basin Boundary Points
• Conclusion
• References
• Figures
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