Rigorous enclosures of rotation numbers by interval methods

Anna  Belova

doi:10.3934/jcd.2016004

Article Contents

2016, Volume 3, Issue 1: 81-91. Doi: 10.3934/jcd.2016004

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Rigorous enclosures of rotation numbers by interval methods

Anna Belova^1,

1.
Box 480, SE-75106, Uppsala

Received: August 31, 2015

Revised: February 29, 2016

Published: December 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 37E45, 37E10, 65G30.

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