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Rigorous enclosures of rotation numbers by interval methods.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2016 (English)In: Journal of Computational Dynamics, ISSN 2158-2491, Vol. 3, no 1, 81-91 p.Article in journal (Refereed) Published
Abstract [en]

We apply set-valued numerical methods to compute an accurate enclosure of the rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points, which is used to check the rationality of the rotation number. A few numerical experiments are presented to show that the implementation of interval methods produces a good enclosure of the rotation number of a circle map.

Place, publisher, year, edition, pages
2016. Vol. 3, no 1, 81-91 p.
Keyword [en]
rotation number, circle map, rigorous computation, interval arithmetic, set-valued mathematics
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-332153DOI: 10.3934/jcd.2016004OAI: oai:DiVA.org:uu-332153DiVA: diva2:1152399
Available from: 2017-10-24 Created: 2017-10-24 Last updated: 2017-10-26
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