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 | |
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.