Nonlinear rotations on a lattice

Nonlinear rotations on a lattice

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...

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Main Authors: Wan Rozali, Wan Nur Fairuz Alwani, Vivaldi, Franco
Format: Article
Language:English
Published: Taylor and Francis 2018
Subjects:
QA300 Analysis
Online Access:http://irep.iium.edu.my/72019/
http://irep.iium.edu.my/72019/
http://irep.iium.edu.my/72019/
http://irep.iium.edu.my/72019/7/Nonlinear%20rotations%20on%20a%20lattice.pdf
id iium-72019
recordtype eprints
spelling iium-720192019-06-20T01:16:27Z http://irep.iium.edu.my/72019/ Nonlinear rotations on a lattice Wan Rozali, Wan Nur Fairuz Alwani Vivaldi, Franco QA300 Analysis 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. Taylor and Francis 2018 Article PeerReviewed application/pdf en http://irep.iium.edu.my/72019/7/Nonlinear%20rotations%20on%20a%20lattice.pdf 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 https://www.tandfonline.com/doi/abs/10.1080/10236198.2018.1459592?journalCode=gdea20 10.1080/10236198.2018.1459592
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA300 Analysis
spellingShingle QA300 Analysis
Wan Rozali, Wan Nur Fairuz Alwani
Vivaldi, Franco
Nonlinear rotations on a lattice
description 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.
format Article
author Wan Rozali, Wan Nur Fairuz Alwani
Vivaldi, Franco
author_facet Wan Rozali, Wan Nur Fairuz Alwani
Vivaldi, Franco
author_sort Wan Rozali, Wan Nur Fairuz Alwani
title Nonlinear rotations on a lattice
title_short Nonlinear rotations on a lattice
title_full Nonlinear rotations on a lattice
title_fullStr Nonlinear rotations on a lattice
title_full_unstemmed Nonlinear rotations on a lattice
title_sort nonlinear rotations on a lattice
publisher Taylor and Francis
publishDate 2018
url http://irep.iium.edu.my/72019/
http://irep.iium.edu.my/72019/
http://irep.iium.edu.my/72019/
http://irep.iium.edu.my/72019/7/Nonlinear%20rotations%20on%20a%20lattice.pdf
first_indexed 2023-09-18T21:42:07Z
last_indexed 2023-09-18T21:42:07Z
_version_ 1777413209853001728

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