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

Not published at VTT

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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

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Ketoja, J. A., & MacKay, R. S. (1989). Fractal boundary for the existence of invariant circles for area-preserving maps: Observations and renormalisation explanation. Physica D: Nonlinear Phenomena, 35(3), 318-334. https://doi.org/10.1016/0167-2789(89)90073-0

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10.1016/0167-2789(89)90073-0

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