Nonlinear rotations on a lattice

Wan Rozali, Wan Nur Fairuz Alwani and Vivaldi, Franco (2018) Nonlinear rotations on a lattice. Journal of Difference Equations and Applications, 24. pp. 1074-1104. ISSN 1023-6198 E-ISSN 1563-5120

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Abstract

We consider a prototypical two-parameter family of invertible maps of Z2, representing rotations with decreasing rotation number. These maps describe the dynamics inside the island chains of a piecewise affine discrete twist map of the torus, in the limit of fine discretisation. We prove that there is a set of full density of points which,depending of the parameter values,are either periodic or escape to infinity. The proof is based on the analysis of an interval-exchange map over the integers, with infinitely many intervals.

Item Type:	Article (Journal)
Additional Information:	8818/72019
Uncontrolled Keywords:	Arithmetic dynamics; stability; periodic orbits
Subjects:	Q Science > QA Mathematics > QA300 Analysis
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences Kulliyyah of Science
Depositing User:	Dr Wan Nur Fairuz Alwani Binti Wan Rozali
Date Deposited:	20 Jun 2019 09:16
Last Modified:	20 Jun 2019 09:16
URI:	http://irep.iium.edu.my/id/eprint/72019

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