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 | |
| Publication status | Published - 1 Jan 1989 |
| MoE publication type | Not Eligible |
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Fractal boundary for the existence of invariant circles for area-preserving maps : Observations and renormalisation explanation. / Ketoja, J. A.; MacKay, R. S.
In: Physica D: Nonlinear Phenomena, Vol. 35, No. 3, 01.01.1989, p. 318-334.Research output: Contribution to journal › Article › Scientific › peer-review
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 -