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

J. A. Ketoja, R. S. MacKay

Research output: Contribution to journalArticleScientificpeer-review

42 Citations (Scopus)


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 languageEnglish
Pages (from-to)318-334
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Issue number3
Publication statusPublished - 1 Jan 1989
MoE publication typeNot Eligible


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