### 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 |
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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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*Physica D: Nonlinear Phenomena*, vol. 35, no. 3, pp. 318-334. https://doi.org/10.1016/0167-2789(89)90073-0

**Fractal boundary for the existence of invariant circles for area-preserving maps : Observations and renormalisation explanation.** / Ketoja, J. A.; MacKay, R. S.

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 -