Clocking convergence to Arnold tongues – the circle map revisited
Mantas Landauskas
Kaunas University of Technology
Minvydas Ragulskis
Kaunas University of Technology
Published 2012-12-15


the circle map
Arnold tongue
rank of a sequence

How to Cite

Landauskas M. and Ragulskis M. (2012) “Clocking convergence to Arnold tongues – the circle map revisited”, Lietuvos matematikos rinkinys, 53(A), pp. 54–59. doi: 10.15388/LMR.A.2012.10.


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.

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