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

18 p, 1.9 MB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles