Dimensions of structurally stable and critical strange non-chaotic attractors

L. N. C. Adamson; Andrew Osbaldestin

doi:10.1088/1751-8113/48/2/025101

Dimensions of structurally stable and critical strange non-chaotic attractors

L. N. C. Adamson, Andrew Osbaldestin

School of Mathematics & Physics

Research output: Contribution to journal › Article › peer-review

346 Downloads (Pure)

Abstract

We provide evidence that the box-counting dimension of a structurally stable strange non-chaotic attractor (SNA) of pinched skew product type is equal to 2 by showing that it has non-negligible area. The argument presented is made more accurate in the study of a piecewise linear SNA. Furthermore we provide evidence that the fractal dimension of a critical SNA is not equal to 2, but in fact lies between 1 and 2. We numerically calculate the box-counting dimension for several critical SNAs, providing further evidence to support this conjecture.

Original language	English
Article number	025101
Pages (from-to)	1-18
Number of pages	18
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	48
Issue number	2
DOIs	https://doi.org/10.1088/1751-8113/48/2/025101
Publication status	Published - 15 Dec 2014

Keywords

Computational physics
Statistical physics and nonlinear systems
dimensions
SNA
renormalization
stable
critical
box-counting

Access to Document

10.1088/1751-8113/48/2/025101

Dimensions
This Accepted Manuscript is available for reuse under a CC BY-NC-ND licence after the 12 month embargo period provided that all the terms and conditions of the licence are adhered to.
Accepted author manuscript (Post-print), 6.59 MBLicence: CC BY-NC-ND

Cite this

@article{4fb11843c4fa4a5a9711cbf8f9bb7899,

title = "Dimensions of structurally stable and critical strange non-chaotic attractors",

abstract = "We provide evidence that the box-counting dimension of a structurally stable strange non-chaotic attractor (SNA) of pinched skew product type is equal to 2 by showing that it has non-negligible area. The argument presented is made more accurate in the study of a piecewise linear SNA. Furthermore we provide evidence that the fractal dimension of a critical SNA is not equal to 2, but in fact lies between 1 and 2. We numerically calculate the box-counting dimension for several critical SNAs, providing further evidence to support this conjecture.",

keywords = "Computational physics, Statistical physics and nonlinear systems, dimensions, SNA, renormalization, stable, critical, box-counting",

author = "Adamson, {L. N. C.} and Andrew Osbaldestin",

year = "2014",

month = dec,

day = "15",

doi = "10.1088/1751-8113/48/2/025101",

language = "English",

volume = "48",

pages = "1--18",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing",

number = "2",

}

TY - JOUR

T1 - Dimensions of structurally stable and critical strange non-chaotic attractors

AU - Adamson, L. N. C.

AU - Osbaldestin, Andrew

PY - 2014/12/15

Y1 - 2014/12/15

N2 - We provide evidence that the box-counting dimension of a structurally stable strange non-chaotic attractor (SNA) of pinched skew product type is equal to 2 by showing that it has non-negligible area. The argument presented is made more accurate in the study of a piecewise linear SNA. Furthermore we provide evidence that the fractal dimension of a critical SNA is not equal to 2, but in fact lies between 1 and 2. We numerically calculate the box-counting dimension for several critical SNAs, providing further evidence to support this conjecture.

AB - We provide evidence that the box-counting dimension of a structurally stable strange non-chaotic attractor (SNA) of pinched skew product type is equal to 2 by showing that it has non-negligible area. The argument presented is made more accurate in the study of a piecewise linear SNA. Furthermore we provide evidence that the fractal dimension of a critical SNA is not equal to 2, but in fact lies between 1 and 2. We numerically calculate the box-counting dimension for several critical SNAs, providing further evidence to support this conjecture.

KW - Computational physics

KW - Statistical physics and nonlinear systems

KW - dimensions

KW - SNA

KW - renormalization

KW - stable

KW - critical

KW - box-counting

U2 - 10.1088/1751-8113/48/2/025101

DO - 10.1088/1751-8113/48/2/025101

M3 - Article

SN - 1751-8113

VL - 48

SP - 1

EP - 18

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 2

M1 - 025101

ER -

Dimensions of structurally stable and critical strange non-chaotic attractors

Abstract

Keywords

Access to Document

Fingerprint

Cite this