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

^*Corresponding author for this work

Not published at VTT

University of Warwick

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

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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10.1016/0167-2789(89)90073-0

Cite this

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

Abstract

Funding

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