Basin boundary metamorphoses: Changes in accessible boundary orbits

Celso Grebogi*, Edward Ott, James A. Yorke

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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 languageEnglish
Pages (from-to)281-300
Number of pages20
JournalNuclear Physics B (Proceedings Supplements)
Volume2
Issue numberC
DOIs
Publication statusPublished - Nov 1987

Bibliographical note

Acknowledgements
We 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.

Fingerprint

Dive into the research topics of 'Basin boundary metamorphoses: Changes in accessible boundary orbits'. Together they form a unique fingerprint.

Cite this