Fractal boundary for the existence of invariant circles for area-preserving maps: Observations and renormalisation explanation

J. A. Ketoja; R. S. MacKay

doi:10.1016/0167-2789(89)90073-0

Fractal boundary for the existence of invariant circles for area-preserving maps: Observations and renormalisation explanation

J. A. Ketoja, R. S. MacKay

Not published at VTT

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

43 Citations (Scopus)

Abstract

Breakup of a golden invariant circle is studied in an extended version of the standard map with two parameters. The critical line in parameter space turns out to have a Cantor set of cusps which can be organized in a self-similar tree. A theoretical explanation is conjectured in terms of a horseshoe for a renormalisation operator. The results of some other researchers on similar systems are shown to fit this explanation as well.

Original language	English
Pages (from-to)	318-334
Number of pages	17
Journal	Physica D: Nonlinear Phenomena
Volume	35
Issue number	3
DOIs	https://doi.org/10.1016/0167-2789(89)90073-0
Publication status	Published - 1 Jan 1989
MoE publication type	Not Eligible

Access to Document

10.1016/0167-2789(89)90073-0

Cite this

@article{e074fe152adb4b3d8917f5156eadbe77,

title = "Fractal boundary for the existence of invariant circles for area-preserving maps: Observations and renormalisation explanation",

abstract = "Breakup of a golden invariant circle is studied in an extended version of the standard map with two parameters. The critical line in parameter space turns out to have a Cantor set of cusps which can be organized in a self-similar tree. A theoretical explanation is conjectured in terms of a horseshoe for a renormalisation operator. The results of some other researchers on similar systems are shown to fit this explanation as well.",

author = "Ketoja, {J. A.} and MacKay, {R. S.}",

year = "1989",

month = jan,

day = "1",

doi = "10.1016/0167-2789(89)90073-0",

language = "English",

volume = "35",

pages = "318--334",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier",

number = "3",

}

TY - JOUR

T1 - Fractal boundary for the existence of invariant circles for area-preserving maps

T2 - Observations and renormalisation explanation

AU - Ketoja, J. A.

AU - MacKay, R. S.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - Breakup of a golden invariant circle is studied in an extended version of the standard map with two parameters. The critical line in parameter space turns out to have a Cantor set of cusps which can be organized in a self-similar tree. A theoretical explanation is conjectured in terms of a horseshoe for a renormalisation operator. The results of some other researchers on similar systems are shown to fit this explanation as well.

AB - Breakup of a golden invariant circle is studied in an extended version of the standard map with two parameters. The critical line in parameter space turns out to have a Cantor set of cusps which can be organized in a self-similar tree. A theoretical explanation is conjectured in terms of a horseshoe for a renormalisation operator. The results of some other researchers on similar systems are shown to fit this explanation as well.

UR - http://www.scopus.com/inward/record.url?scp=0009545767&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(89)90073-0

DO - 10.1016/0167-2789(89)90073-0

M3 - Article

AN - SCOPUS:0009545767

VL - 35

SP - 318

EP - 334

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3

ER -

Fractal boundary for the existence of invariant circles for area-preserving maps: Observations and renormalisation explanation

Abstract

Access to Document

Other files and links

Fingerprint

Cite this