Basin boundary metamorphoses

Changes in accessible boundary orbits

Celso Grebogi*, Edward Ott, James A. Yorke

*Corresponding author for this work

Research output: Contribution to journalArticle

2 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

Fingerprint

orbits
fractals
saddles
causes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Basin boundary metamorphoses : Changes in accessible boundary orbits. / Grebogi, Celso; Ott, Edward; Yorke, James A.

In: Nuclear Physics B (Proceedings Supplements), Vol. 2, No. C, 11.1987, p. 281-300.

Research output: Contribution to journalArticle

@article{ebd80057808e4c628b0cf6bb9cdf0ecf,
title = "Basin boundary metamorphoses: Changes in accessible boundary orbits",
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.",
author = "Celso Grebogi and Edward Ott and Yorke, {James A.}",
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.",
year = "1987",
month = "11",
doi = "10.1016/0920-5632(87)90024-7",
language = "English",
volume = "2",
pages = "281--300",
journal = "Nuclear Physics B (Proceedings Supplements)",
issn = "0920-5632",
publisher = "Elsevier",
number = "C",

}

TY - JOUR

T1 - Basin boundary metamorphoses

T2 - Changes in accessible boundary orbits

AU - Grebogi, Celso

AU - Ott, Edward

AU - Yorke, James A.

N1 - 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.

PY - 1987/11

Y1 - 1987/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=45949113204&partnerID=8YFLogxK

U2 - 10.1016/0920-5632(87)90024-7

DO - 10.1016/0920-5632(87)90024-7

M3 - Article

VL - 2

SP - 281

EP - 300

JO - Nuclear Physics B (Proceedings Supplements)

JF - Nuclear Physics B (Proceedings Supplements)

SN - 0920-5632

IS - C

ER -