Abstract
Basin boundaries sometimes undergo sudden metamorphoses. These metamorphoses can lead to the conversion of a smooth basin boundary to one which is fractal, or else can cause a fractal basin boundary to suddenly jump in size and change its character (although remaining fractal). For an invertible map in the plane, there may be an infinite number of saddle periodic orbits in a basin boundary that is fractal. Nonetheless, we have found that typically only one of them can be reached or "accessed" directly from a given basin. The other periodic orbits are buried beneath infinitely many layers of the fractal structure of the boundary. The boundary metamorphoses which we investigate are characterized by a sudden replacement of the basin boundary's accessible orbit.
Original language | English |
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Pages (from-to) | 281-300 |
Number of pages | 20 |
Journal | Nuclear Physics B (Proceedings Supplements) |
Volume | 2 |
Issue number | C |
DOIs | |
Publication status | Published - Nov 1987 |
Bibliographical note
AcknowledgementsWe would like to thank Shen-Teng Yang for making the pictures of fig. 1 and Bae-Sig Park for numerically determining the dimension of the basin boundary corresponding to fig. 2b. This work was supported by the Department of Energy (Office of Basic Energy Sciences), DARPA under NIMPP, and the Office of Naval Research.