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

J. A. Ketoja*, R. S. MacKay

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

44 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 languageEnglish
Pages (from-to)318-334
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume35
Issue number3
DOIs
Publication statusPublished - 1 Jan 1989
MoE publication typeNot Eligible

Funding

J. Ketoja is grateful to the Academy of Finland and the Emil Aaltcnen Foundation for their financial support. The computations were made on equipment granted by the UK Science and Engineering Research Council.

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