An algorithm to compute rotation intervals of circle maps
Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Borrós-Culllell, Salvador (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Date: |
2021 |
Abstract: |
In this article we present an efficient algorithm to compute rotation intervals of circle maps of degree one. It is based on the computation of the rotation number of a monotone circle map of degree one with a constant section. The main strength of this algorithm is that it computes exactly the rotation interval of a natural subclass of the continuous non-invertible degree one circle maps. We also compare our algorithm with other existing ones by plotting the Devil's Staircase of a one-parameter family of maps and the Arnold Tongues and rotation intervals of some special non-differentiable families, most of which were out of the reach of the existing algorithms that were centred around differentiable maps. |
Grants: |
Ministerio de Ciencia e Innovación MTM2017-86795-C3-1-P Ministerio de Ciencia e Innovación MDM-2014-0445
|
Note: |
Altres ajuts: acords transformatius de la UAB |
Rights: |
Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original. |
Language: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Subject: |
Rotation number ;
Circle maps ;
Nondecreasing degree one lifting ;
Algorithm |
Published in: |
Communications in nonlinear science and numerical simulation, Vol. 102 (November 2021) , art. 105915, ISSN 1007-5704 |
DOI: 10.1016/j.cnsns.2021.105915
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Record created 2021-09-08, last modified 2023-10-01