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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| Format: | Article |
| Language: | English |
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Taylor and Francis
2018
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| Online Access: | http://irep.iium.edu.my/72019/ http://irep.iium.edu.my/72019/7/Nonlinear%20rotations%20on%20a%20lattice.pdf |
| _version_ | 1848787551032180736 |
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| 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 |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T17:26:43Z |
| format | Article |
| id | iium-72019 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T17:26:43Z |
| publishDate | 2018 |
| publisher | Taylor and Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| spellingShingle | QA300 Analysis Wan Rozali, Wan Nur Fairuz Alwani Vivaldi, Franco Nonlinear rotations on a lattice |
| title | 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_short | Nonlinear rotations on a lattice |
| title_sort | nonlinear rotations on a lattice |
| topic | QA300 Analysis |
| 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 |