Basin boundary metamorphoses: Changes in accessible boundary orbits

Celso Grebogi, Edward Ott, James A. Yorke

Research output: Contribution to journalArticlepeer-review

208 Citations (Scopus)


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, or else can 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 languageEnglish
Pages (from-to)243-262
Number of pages20
JournalPhysica. D, Nonlinear Phenomena
Issue number1-3
Publication statusPublished - Jan 1987


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