Strange saddles and the dimensions of their invariant-manifolds

G H Hsu, E Ott, C Grebogi

Research output: Contribution to journalArticle

128 Citations (Scopus)

Abstract

Nonattracting chaotic sets play a fundamental role in typical dynamical systems. They occur, for example, in the form of chaotic transient sets and fractal basin boundaries. The subject of this paper is the dimensions of these sets and of their stable and unstable manifolds. Numerical experiments are performed to determine these dimensions. The results are consistent with a conjectured formulae expressing the dimensions in terms of Lyapunov exponents and the transient life-time associated with the strange saddle.
Original languageEnglish
Pages (from-to)199-204
Number of pages6
JournalPhysics Letters A
Volume127
Issue number4
DOIs
Publication statusPublished - 22 Feb 1988

Cite this

Strange saddles and the dimensions of their invariant-manifolds. / Hsu, G H ; Ott, E ; Grebogi, C .

In: Physics Letters A, Vol. 127, No. 4, 22.02.1988, p. 199-204.

Research output: Contribution to journalArticle

Hsu, G H ; Ott, E ; Grebogi, C . / Strange saddles and the dimensions of their invariant-manifolds. In: Physics Letters A. 1988 ; Vol. 127, No. 4. pp. 199-204.
@article{4dfd62870da14addbe443cf76688577f,
title = "Strange saddles and the dimensions of their invariant-manifolds",
abstract = "Nonattracting chaotic sets play a fundamental role in typical dynamical systems. They occur, for example, in the form of chaotic transient sets and fractal basin boundaries. The subject of this paper is the dimensions of these sets and of their stable and unstable manifolds. Numerical experiments are performed to determine these dimensions. The results are consistent with a conjectured formulae expressing the dimensions in terms of Lyapunov exponents and the transient life-time associated with the strange saddle.",
author = "Hsu, {G H} and E Ott and C Grebogi",
year = "1988",
month = "2",
day = "22",
doi = "10.1016/0375-9601(88)90102-8",
language = "English",
volume = "127",
pages = "199--204",
journal = "Physics Letters A",
issn = "0375-9601",
publisher = "Elsevier",
number = "4",

}

TY - JOUR

T1 - Strange saddles and the dimensions of their invariant-manifolds

AU - Hsu, G H

AU - Ott, E

AU - Grebogi, C

PY - 1988/2/22

Y1 - 1988/2/22

N2 - Nonattracting chaotic sets play a fundamental role in typical dynamical systems. They occur, for example, in the form of chaotic transient sets and fractal basin boundaries. The subject of this paper is the dimensions of these sets and of their stable and unstable manifolds. Numerical experiments are performed to determine these dimensions. The results are consistent with a conjectured formulae expressing the dimensions in terms of Lyapunov exponents and the transient life-time associated with the strange saddle.

AB - Nonattracting chaotic sets play a fundamental role in typical dynamical systems. They occur, for example, in the form of chaotic transient sets and fractal basin boundaries. The subject of this paper is the dimensions of these sets and of their stable and unstable manifolds. Numerical experiments are performed to determine these dimensions. The results are consistent with a conjectured formulae expressing the dimensions in terms of Lyapunov exponents and the transient life-time associated with the strange saddle.

U2 - 10.1016/0375-9601(88)90102-8

DO - 10.1016/0375-9601(88)90102-8

M3 - Article

VL - 127

SP - 199

EP - 204

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 4

ER -