Clocking convergence to Arnold tongues – the circle map revisited
Computational techniques based on ranks of Hankel matrices is used to study the convergence to Arnold tongues. It appears that the process of convergence to the phaselocked mode is far from being trivial. The stable, the unstable and the manifold of nonasymptotic convergence intertwine in the parame...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2012-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/14870 |
| _version_ | 1818343532392349696 |
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| author | Mantas Landauskas Minvydas Ragulskis |
| author_facet | Mantas Landauskas Minvydas Ragulskis |
| author_sort | Mantas Landauskas |
| collection | DOAJ |
| description | Computational techniques based on ranks of Hankel matrices is used to study the convergence to Arnold tongues. It appears that the process of convergence to the phaselocked mode is far from being trivial. The stable, the unstable and the manifold of nonasymptotic convergence intertwine in the parameter plane of the circle map. Pseudoranks of Hankel matrices carry important physical information about transient processes taking place in discrete nonlinear iterative maps. These pictures in the parameter plane are also beautiful from the aesthetical point of view. |
| first_indexed | 2024-12-13T16:32:05Z |
| format | Article |
| id | doaj.art-2f8637625a054b09a9a25e262914290b |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-12-13T16:32:05Z |
| publishDate | 2012-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-2f8637625a054b09a9a25e262914290b2022-12-21T23:38:29ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2012-12-0153A10.15388/LMR.A.2012.10Clocking convergence to Arnold tongues – the circle map revisitedMantas Landauskas0Minvydas Ragulskis1Kaunas University of TechnologyKaunas University of TechnologyComputational techniques based on ranks of Hankel matrices is used to study the convergence to Arnold tongues. It appears that the process of convergence to the phaselocked mode is far from being trivial. The stable, the unstable and the manifold of nonasymptotic convergence intertwine in the parameter plane of the circle map. Pseudoranks of Hankel matrices carry important physical information about transient processes taking place in discrete nonlinear iterative maps. These pictures in the parameter plane are also beautiful from the aesthetical point of view.https://www.journals.vu.lt/LMR/article/view/14870the circle mapArnold tonguerank of a sequence |
| spellingShingle | Mantas Landauskas Minvydas Ragulskis Clocking convergence to Arnold tongues – the circle map revisited Lietuvos Matematikos Rinkinys the circle map Arnold tongue rank of a sequence |
| title | Clocking convergence to Arnold tongues – the circle map revisited |
| title_full | Clocking convergence to Arnold tongues – the circle map revisited |
| title_fullStr | Clocking convergence to Arnold tongues – the circle map revisited |
| title_full_unstemmed | Clocking convergence to Arnold tongues – the circle map revisited |
| title_short | Clocking convergence to Arnold tongues – the circle map revisited |
| title_sort | clocking convergence to arnold tongues the circle map revisited |
| topic | the circle map Arnold tongue rank of a sequence |
| url | https://www.journals.vu.lt/LMR/article/view/14870 |
| work_keys_str_mv | AT mantaslandauskas clockingconvergencetoarnoldtonguesthecirclemaprevisited AT minvydasragulskis clockingconvergencetoarnoldtonguesthecirclemaprevisited |