Journal of Computational Dynamics (JCD)

Rigorous enclosures of rotation numbers by interval methods

Pages: 81 - 91, Volume 3, Issue 1, June 2016      doi:10.3934/jcd.2016004

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Anna Belova - Box 480, SE-75106, Uppsala, Sweden (email)

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.

Keywords:  Rotation number, circle map, rigorous computation, interval arithmetic, set-valued mathematics.
Mathematics Subject Classification:  Primary: 37E45, 37E10, 65G30.

Received: September 2015;      Revised: March 2016;      Available Online: September 2016.